# Yonghong Wu's research while affiliated with Curtin University and other places

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## Publications (291)

The digital economy can change the proportions and types of production factors, gradually replace traditional backward production factors, reconstruct the division of labor and cooperation system, and improve productivity, which is an important basis for balanced and sufficient development. This paper measures the comprehensive level of the digital...

In this paper, we consider the existence of positive solutions for a semipositone third-order nonlinear ordinary differential equation on time scales. In suitable growth conditions, by considering the properties on time scales and establishing a special cone, some new results on the existence of positive solutions are established when the nonlinear...

In the study of many real-world problems such as engineering design and industrial process control, one often needs to select certain elements/controls from a feasible set in order to optimize the design or system based on certain criteria [...]

The \(L_p\) dual curvature measures were recently introduced by Lutwak et al. (Adv Math 329:85-132, 2018) to unify the classical theory of mixed volumes and the newer theory of dual mixed volumes of convex bodies. However, the associated \(L_p\) dual Minkowski problems for many important special cases remain open problems. They are analytically equ...

In this paper, we establish a new result on the existence of the radial solutions for an eigenvalue problem of singular augmented Hessian equation. By adopting some suitable growth conditions and combining the method of upper and lower solutions, we derive a sufficient condition for the existence of radial solutions of the equations in which the no...

In this paper, we focus on the existence of positive solutions for a boundary value problem of the changing-sign differential equation on time scales. By constructing a translation transformation and combining with the properties of the solution of the nonhomogeneous boundary value problem, we transfer the changing-sign problem to a positone proble...

In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fix...

In this paper, we focus on the k-convex solution to the following boundary blow-up k-Hessian equation with the logarithmic nonlinearity and singular weights $$\begin{aligned} \left\{ \begin{array}{ll} &{}S_{k}\left( D^{2}u\right) =H(x)u^{k}\left( \ln u\right) ^{\beta }>0,\ \text {in} \ \Omega ,\\ &{} u=\infty , \ \text { on} \ \partial \Omega , \en...

This study presents a distributionally robust optimization model to address the ramp metering problem with uncertain traffic demand flows. The aim of this model is to minimize the total travel delay of the system based on the macroscopic cell transmission model (CTM) of traffic flow. In our model, the only required data is the partial distributiona...

In this paper, we consider the iterative properties of positive solutions for a general Hadamard-type singular fractional turbulent flow model involving a nonlinear operator. By developing a double monotone iterative technique we firstly establish the uniqueness of positive solutions for the corresponding model. Then we carry out the iterative anal...

How do investors require a distribution of the wealth among multiple risky assets while facing the risk of the uncontrollable payment for random liabilities? To cope with this problem, firstly, this paper explores the approach of asset-liability management under the state-dependent risk aversion with only risky assets, which has been considered und...

Ramp metering offers great potential to mitigate traffic congestion and improve freeway management efficiency under traffic congestion conditions. This paper proposes an optimization program for freeway dynamic ramp metering based on Cell Transmission Model (CTM). This problem has been formulated as a discrete time optimal control problem with smoo...

In this paper, we are concerned with the radial solutions for the eigenvalue problem of a singular k-Hessian equation. By constructing the upper and lower solutions of the k-Hessian equation, the existence of a radial solution for the eigenvalue problem is established via Schauder’s fixed point theorem under the case where the nonlinearity possesse...

The main purpose of this work is to develop a numerical solution method for solving a class of nonlinear free final time fractional optimal control problems. This problem is subject to equality and inequality constraints in canonical forms, and the orders in the fractional system can be different. For this problem, we first show that, by a time-sca...

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dual cone in Hilbert spaces. We first discuss the relation between the isotonicity of the projection onto the cone and its dual cone. Some sufficient condit...

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach.

We study a defined contribution pension system with the return of premium clauses, which is embedded with two administrative fees: the charge on balance and the charge on flow. The fund wealth is invested in financial market with a riskless asset and a risky asset modelled by a constant elasticity of variance process. We use the Weibull model to ch...

We are concerned with the nonlinear Schrödinger-Poisson equation $$\begin{cases}-\Delta u+(V(x)-\lambda)u+\phi(x)u=f(u),\\-\Delta\phi=u^{2},\lim\limits_{\vert x\vert\rightarrow+\infty}\phi(x)=0,x\in \mathbb{R}^{3},\end{cases}\ {\mathrm{(P)}}$$ where λ is a parameter, V (x) is an unbounded potential and f (u) is a general nonlinearity. We prove the...

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our...

A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solutio...

This paper concerns the pricing of volatility and variance swaps with discrete sampling times using a hybrid Heston-CIR model with Markov-modulated jump-diffusion. We extend the regime-switching Heston stochastic volatility model by further considering the Cox-Ingersoll-Ross (CIR) stochastic interest rate with jump diffusion. The market parameters,...

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases a...

In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonli...

In this paper, we consider the iterative properties of solution for a general singular n-Hessian equation with decreasing nonlinearity. By introducing a double iterative technique, we firstly establish the criterion of the existence for unique solution, and then study the convergence properties of solution as well as error estimation and the conver...

In this paper, we consider the iterative algorithm for a boundary value problem of -order fractional differential equation with mixed integral and multipoint boundary conditions. Using an iterative technique, we derive an existence result of the uniqueness of the positive solution, then construct the iterative scheme to approximate the positive sol...

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the g...

In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the opti...

The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. In the functional setting as close as possible to the physical energy spaces...

In this paper, the isotonicity of the proximity operator and its applications are discussed. We first establish a few new conditions of the mappings such that their proximity operators are isotone with respect to orders induced different minihedral cones. Some properties and examples for these conditions are then introduced. We especially consider...

In the paper, we establish the uniqueness of positive solutions for a model of higher-order singular fractional boundary value problems with p-Laplacian operator. The equation includes the Caputo and the Riemann-Liouville fractional derivative. The boundary conditions contain Riemann-Stieltjes integrals and nonlocal infinite-point boundary conditio...

Motivated by the recent works on proximity operators and isotone projection cones, in this paper, we discuss the isotonicity of the proximity operator in quasi-lattices, endowed with general cones. First, we show that Hilbert spaces, endowed with general cones, are quasi-lattices, in which the isotonicity of the proximity operator with respect to o...

In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equati...

In this paper, we are concerned with the existence of the maximum and minimum iterative solutions for a tempered fractional turbulent flow model in a porous medium with nonlocal boundary conditions. By introducing a new growth condition and developing an iterative technique, we establish new results on the existence of the maximum and minimum solut...

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, a linear weak damping and superlinear source. Finite time blow-up results have been obtained for the case in which the initial energy Eð0Þ M, where M is a positive constant. By utilizing Levine's classical concavity method, we give a new blo...

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, a linear weak damping and superlinear source. Finite time blow-up results have been obtained for the case in which the initial energy \(E(0)\le M\), where M is a positive constant. By utilizing Levine’s classical concavity method, we give a...

We investigate a continuous dynamic model associated with a firm size term and with an external factor term, which possesses the following peculiarities: the drift term is dominated by the principal’s investment strategy and the agent’s effort; the volatility term relies on the function \(\sqrt{G^2(t)+z_t}\) in which \(G(t)\ge 0\) is a continuously...

Abstract In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives. The boundary conditions are constituted by Riemann–Stieltjes integral boundary conditions. The existence and multiplicity of positive solutions are derived via em...

In this paper, we focus on the existence of positive solutions for a class of weakly singular Hadamard-type fractional mixed periodic boundary value problems with a changing-sign singular perturbation. By using nonlinear analysis methods combining with some numerical techniques, we further discuss the effect of the perturbed term for the existence...

Abstract This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schaud...

This paper investigates the time-consistent optimal control of a mean–variance asset-liability management problem in a regime-switching jump-diffusion market. The investor (a company) is investing in the market with one risk-less bond and one risky stock while subject to an uncontrollable liability. The risky stock and the liability processes are d...

Abstract We consider the existence of solutions for the following Hadamard-type fractional differential equations: { D α H u ( t ) + q ( t ) f ( t , u ( t ) , H D β 1 u ( t ) , H D β 2 u ( t ) ) = 0 , 1 < t < + ∞ , u ( 1 ) = 0 , D α − 2 H u ( 1 ) = ∫ 1 + ∞ g 1 ( s ) u ( s ) d s s , D α − 1 H u ( + ∞ ) = ∫ 1 + ∞ g 2 ( s ) u ( s ) d s s , $$ \textsty...

This paper is concerned with the study of the Cauchy problem to a multi-dimensional P1-approximation model. Based on a known global well-posedness (Danchin and Ducomet in J Evol Equ 14:155–195, 2014), in \(L^{2}\)-critical regularity framework the time decay rates of the constructed global strong solutions are obtained if the low frequencies of the...

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given,...

In this paper, we focus on the convergence analysis of the unique solution for a Dirichlet problem of the general k-Hessian equation in a ball. By introducing some suitable growth conditions and developing a new iterative technique, the unique solution of the k-Hessian equation is obtained. Then we carry out the convergence analysis for the iterati...

This article is concerned with a class of singular nonlinear fractional boundary value problems with p -Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary c...

In this paper, we establish some new results for the existence and nonexistence of radial large positive solutions for the modified Schrödinger system with a nonconvex diffusion term. Our main tools are the successive iteration technique and dual approach. A necessary and sufficient condition for the existence of radial large positive solutions is...

Abstract In this paper, we consider a new class of singular nonlinear higher order fractional boundary value problems supplemented with sum of Riemann–Stieltjes integral type and nonlocal infinite-point discrete type boundary conditions. The fractional derivative of different orders is involved in the nonlinear terms and boundary conditions, and th...

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations...

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the correspondi...

This paper further studies axiomatic characterizations of L-fuzzy rough sets, where L denotes a residuated lattice. Single axioms for upper L-fuzzy rough approximation operators are investigated in two different approaches, which describe upper L-fuzzy approximation operators with ordinary L-fuzzy operations and L-fuzzy product operation, respectiv...

In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term
where is a bounded domain in ( ) with a Dirichlet boundary condition. Under suitable assumptions on the initial data and the relaxation function g, we obtain the global existence an...

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enoug...

Abstract In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source: utt+Δ2u−∫0tg(t−τ)Δ2u(τ)dτ+|ut|m−2ut=|u|p−2u,in Ω×(0,T). $$ u_{tt}+\Delta ^{2} u- \int _{0}^{t} g(t-\tau )\Delta ^{2} u(\tau )\,\mathrm{d} \tau + \vert u_{t} \vert ^{m-2}u_{t}= \vert...

In this article, we study a class of nonlinear fractional differential equations with mixedtype boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction mapping principle based on some availab...

Abstract In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are...

In this paper, we study a class of nonlinear singular system with coupled integral boundary condition. Based on the Guo–Krasnosel'skii fixed point theorem, some new results on the existence of symmetric positive solutions for the coupled singular system are obtained. The impact of the two different parameters on the existence of symmetric positive...

In this paper, we study the existence and asymptotic behavior of radial solutions for a class of nonlinear Schrödinger elliptic equations on infinite domains describing the gyre of geophysical fluid flows. The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.

In this paper, we focus on the iterative scheme and error estimation of positive solutions for a class of p-Laplacian fractional order differential equation subject to Riemann-Stieltjes integral boundary condition. Under a weaker growth condition of nonlinearity, by using a monotone iterative technique, we first establish a new result on the suffic...

In this paper, we prove a logarithmic improvement of regularity criterion only in terms of the pressure in Morrey–Campanato spaces for the Cauchy problem to the incompressible MHD equations.

In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball. Under some suitable local growth conditions for nonlinearity, several new results are obtained by using the fixed point theorem.

In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative technique. Furthermore, the iterative sequence of the solution and the error estimation of the system are given. Then we use this new result to...

We are concerned with the study of the Cauchy problem to the 3D compressible Hall-magnetohydrodynamic system. We first establish the unique global solvability of strong solutions to the system when the initial data are close to a stable equilibrium state in critical Besov spaces. Furthermore, under a suitable additional condition involving only the...

In this paper, we focus on the convergence analysis and error estimation for the unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the probl...

In this paper, we study a three-dimensional (3D) viscoelastic wave
equation with nonlinear weak damping, supercritical sources and
prescribed past history $u_0(x,t)$, $t\leq 0$:
\[
u_{tt}-k(0)\D u-\int_0^{+\infty} k'(s)\D u(t-s)d s +|u_t|^{m-1}u_t=|u|^{p-1}u,\quad \textrm{in }\Omega\times (0,T),
\]
where the relaxation function $k$ is monotone decr...

By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann-Stielt...

In this paper, we establish some new results on the existence and nonexistence of radial large positive solutions for a modified Schrödinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach. The necessary and sufficient condition for the existence of radial large positive solutions is established. Our...

In this paper, we study the risk aversion on valuing the single-name credit derivatives with the fast-scale stochastic volatility correction. Two specific utility forms, including the exponential utility and the power utility, are tested as examples in our work. We apply the asymptotic approximation to obtain the solution of the non-linear PDE, and...

By introducing a growth condition and using an iterative technique, we establish the results for the nonexistence and existence of positive entire blow-up solutions for a Schrödinger equation involving a nonlinear operator. Our main results improve and extend some existing works. In addition, we also give an example to illustrate our results.

In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic
equations:
\[
u_{t}-a\D u_t-\D u+b u=k(t)|u|^{p-2}u,\quad (x,t)\in\Omega\times (0,T),
\]
where $a\geq 0$, $b>-\lambda_1$ with $\lambda_1$ being the principal eigenvalue for $-\Delta$ on $H_0^1(\Omega)$ and $k(t)>0$. By using the potential well...

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integra...

In this paper, we investigate the existence of nontrivial solutions for a class of fractional advection–dispersion systems. The approach is based on the variational method by introducing a suitable fractional derivative Sobolev space. We take two examples to demonstrate the main results.

This paper is concerned with the uniqueness of positive solutions for a class of singular fractional differential equations with integral boundary conditions. The nonlinear term and boundary conditions of fractional differential equation contain the fractional order derivatives. The uniqueness of positive solutions is derived by the fixed point the...

In this paper, we study a class of fractional semilinear integro-differential equations of order

In this paper, we consider the existence of nontrivial solutions for a class of fractional advection–dispersion equations. A new existence result is established by introducing a suitable fractional derivative Sobolev space and using the critical point theorem.

In this paper, as the extension of the isotonicity of the metric projection, the isotonicity characterizations with respect to two arbitrary order relations induced by cones of the metric projection operator are studied in Hilbert spaces, when one cone is a subdual cone and some relations between the two orders hold. Moreover, if the metric project...

In this paper, we are concerned with the regularity criterion for weak solutions to the 3D incompressible MHD equations. We show that if any two groups functions of \((\partial _{1}u_{1}, \partial _{1}b_{1})\), \((\partial _{2}u_{2}, \partial _{2}b_{2})\) and \((\partial _{3}u_{3}, \partial _{3}b_{3})\) belong to the space \(L^{\theta }([0,T);L^{r}...

We give some background of fractional Cauchy problems and correct an existing result of Cauchy problem for the fractional differential inequality, and we also give an example to illustrate our statement.

In this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtain...

In this paper, we consider the initial boundary value problem for a class of thin-film equations in Rn with a p-Laplace term and a nonlocal source term |u|q-2u-1|Ω|∫Ω|u|q-2udx. We prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time. We also obtain the upper bounds for the blow-up time.

The present paper is dedicated to the study of the Cauchy problems for the three-dimensional compressible nematic liquid crystal flow. We obtain the global existence and the optimal decay rates of smooth solutions to the system under the condition that the initial data in lower regular spaces are close to the constant equilibrium state. Our main me...

This paper demonstrates the existence of Feigenbaum's constants in reverse bifurcation for fractional-order Rössler system. First, the numerical algorithm of fractional-order Rössler system is presented. Then, the definition of Feigenbaum's constants in reverse bifurcation is provided. Third, in order to observe the effect of fractional-order to Fe...

We study the 2-dimensional dual Minkowski problem, which is the following nonlinear problem on unit circleu″+u=g(θ)u−1(u2+u′2)(2−k)/2,θ∈S,
for any given positive continuous function g(θ) with 2π/m-periodic. We prove that it is solvable for all k∈(1,+∞) and m∈{3,4,5⋯}.