Pengyu Chen

Northwest Normal University · Department of Mathematics

This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related S-asymptotically \(\omega \)-periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can...

A highly nonlinear lattice p-Laplacian equation driven by superlinear noise is considered. By using an appropriate stopping time technique and the dissipativeness of the nonlinear drift terms, we establish the global existence and uniqueness of the solutions in \(C\bigg ([\tau ,\infty ), L^2(\Omega , \ell ^2)\bigg )\cap L^p\bigg (\Omega , L_{\text...

This paper is devoted to study the asymptotic behavior of solutions to a class of stochastic BBM equations driven by nonlinear or linear colored noise defined on a three-dimensional unbounded channel. We first prove existence of compact pullback random attractors of the stochastic BBM equation driven by nonlinear colored noise and then establish th...

In this paper, we consider a class of nonlinear time-space fractional reaction-diffusion equations by transforming the time-space fractional reaction-diffusion equations into an abstract evolution equations in a fractional Sobolev space. Based on operator semigroup theory, the local uniqueness of mild solutions to the reaction-diffusion equations i...

This paper is concerned with the long term behavior of the solutions of the non-autonomous Benjamin-Bona-Mahony equation driven by nonlinear colored noise with continuous coefficients defined on three-dimensional unbounded channels. The solutions of the equation are not unique and hence generate a multivalued non-autonomous random dynamical system....

In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic...

In this paper, we study the asymptotic behavior of solutions of fractional nonclassical diffusion equations with delay driven by additive noise defined on unbounded domains. We first prove the uniform compactness of pullback random attractors of the equation with respect to noise intensity and time delay, and then establish the upper semi-continuit...

This paper deals with the long-time dynamics for a class of highly nonlinear fractional nonclassical diffusion equations with nonlinear colored noise and time delay defined on the whole space Rn. The existence and uniqueness of tempered pullback random attractors of the equations are established in C([−ρ,0],Hα(Rn)) (ρ>0 and α∈(0,1)) for polynomial...

This paper is concerned with the asymptotic behavior of the solutions to a class of non-autonomous non-local fractional stochastic p-Laplacian equations with delay driven by linear multiplicative white noise on the entire space Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usep...

This paper deals with the well-posedness and existence of attractors of a class of stochastic diffusion equations with fractional damping and time-varying delay on unbounded domains. We first prove the well-posedness and the existence of a continuous non-autonomous cocycle for the equations and the uniform estimates of solutions and the derivative...

In this paper, we investigate the global existence, uniqueness and asymptotic stability of time periodic classical solution for a class of extended Fisher-Kolmogorov equations with delays and general nonlinear term. We establish a general framework to investigate the asymptotic behavior of time periodic solutions for nonlinear extended Fisher-Kolmo...

In this paper, we investigate a class of impulsive differential equations with state-dependent delay under analytic semigroup in Banach spaces. The existence and uniqueness of classical solution is obtained under the assumptions that nonlinear function and impulsive map are Lipschitz continuous. On these assumptions, we further study the existence...

In this paper, we investigate the blowup, as well as global existence, and uniqueness of mild solutions for the initial-boundary value problem to a class of fractional extended Fisher–Kolmogorov equations with a general nonlinear term. We establish a general framework to find the global mild solutions for fractional extended Fisher–Kolmogorov equat...

We consider Lipschitz stability of zero solutions to the initial value problem of nonlinear ordinary differential equations with non-instantaneous impulses on ordered Banach spaces. Using Lyapunov function, Lipschitz stability of zero solutions to nonlinear ordinary differential equation with non-instantaneous impulses is obtained.

In this article, we apply the perturbation technique and monotone iterative method in the presence of the lower and the upper solutions to discuss the existence of the minimal and maximal mild solutions to the retarded evolution equations involving nonlocal and impulsive conditions in an ordered Banach space X $$\displaylines{ u'(t)+Au(t)= f(t,u(t)...

In this paper, we provide some sufficient conditions for the existence, uniqueness and asymptotic stability of time !-periodic mild solutions for a class of non-autonomous evolution equation with multi-delays. This work not only extend the autonomous evolution equation with multi-delays studied in [37] to non-autonomous cases, but also greatly weak...

This paper deals with the Cauchy problem to a class of nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness in infinite-dimensional Banach spaces. Combining the theory of fractional calculus and evolution families, the fixed point theorem with respect to convex-power condensing...

This paper investigates the Cauchy problem to a class of stochastic non-autonomous evolution equations of parabolic type governed by noncom- pact evolution families in Hilbert spaces. Combining the theory of evolution families, the fixed point theorem with respect to convex-power condensing op- erator and a new estimation technique of the measure o...

In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introducing a new Green’s...

In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of non-autonomous evolution system of parabolic type with nonlocal conditions in Banach spaces. Sufficient conditions of existence of mild solutions and approximate controllability for the desired problem are presented by introd...

The aim of this paper is to discuss the existence of mild solutions for a class of time fractional non-autonomous evolution equations with nonlocal conditions and measure of noncompactness in infinite-dimensional Banach spaces. Combining the theory of fractional calculus and evolution families, the fixed point theorem with respect to k-set-contract...

In this paper, we study the Cauchy problem to a class of non-autonomous evolution equations of parabolic type with non-instantaneous impulses in Banach spaces, where the operators in linear part (possibly unbounded) depend on time t and generate an evolution family. New existence result of piecewise continuous mild solutions is established under mo...

In this paper, we study the initial value problem to a class of non-autonomous parabolic evolution equations with non-instantaneous impulses in Banach spaces, where the operators in linear part (possibly unbounded) depend on time t and generate an noncompact evolution family. Some new existence results of piecewise continuous mild solutions are est...

The aim of this paper is to discuss the existence of mild solutions and positive mild solutions for a general class of semilinear fractional retarded evolution equations subjected to mixed nonlocal plus local initial conditions on infinite dimensional Banach spaces. Under the situation that the nonlinear term and nonlocal function satisfy some appr...

In this paper, we are concerned with the periodic boundary value problem of fractional differential equations on ordered Banach spaces. By introducing a concept of upper and lower solutions, we construct a new monotone iterative technique for the periodic boundary value problems of fractional differential equation, and obtain the existence of solut...

The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert space. Combined with the theory of stochastic analysis and operator semigroups, a generalized Darbo’s fixed point theorem and a...

This paper deals with the following Cauchy problem to nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness $$ \left\{\begin{array}{ll} ^CD^{\alpha}_tu(t)+A(t)u(t)= f(t,u(t),(Tu)(t), (Su)(t)),\quad t\in [0,a], \\[12pt] u(0)=A^{-1}(0)u_0 \end{array} \right. $$ in infinite-dimensi...

In this paper, we investigate the global existence, uniqueness and asymptotic stability of time $\omega$-periodic classical solution for a class of extended Fisher-Kolmogorov equations with delays and general nonlinear term. We establish a general framework to find time $\omega$-periodic solutions for nonlinear extended Fisher-Kolmogorov equations...

Abstract This paper discusses the existence and uniqueness of positive solutions for a periodic boundary value problem of a fractional differential equation in an ordered Banach space E. The existence and uniqueness results of solutions for the associated linear periodic boundary value problem of the fractional differential equation are established...

In this article, we consider a class of fractional non-autonomous integro-differential evolution equation of Volterra type in a Banach space E, where the operators in linear part (possibly unbounded) depend on time t. Combining the theory of fractional calculus, operator semigroups and measure of noncompactness with Sadovskii’s fixed point theorem,...

This paper is concerned with the continuous dependence of mild solutions on initial values and orders for a general class of initial boundary-value problem to fractional extended Fisher–Kolmogorov equation. The results obtained in this paper can be considered as a contribution to this emerging field.

We use the fixed point index theory of condensing mapping in cones discuss the existence of positive solutions for the following boundary value problem of fractional differential equations in a Banach space E$$\begin{aligned} \left\{ \begin{array}{ll} -D^{\,\beta }_{0^{+}}u(t)=f(t,u(t)),\quad t\in J, \\ u(0)=u^{\prime }(0)=\theta ,\quad u(1)=\rho \...

This paper deals with the existence of mild solutions for a class of fractional stochastic evolution equations with nonlocal initial conditions and and noncompact semigroups in a real separable Hilbert space. We assume that the linear part generates an equicontinuous -semigroup, and the nonlinear functions satisfy some appropriate growth conditions...

In this article, we are concerned with the initial value problem of a class of evolution equations with non-instantaneous impulses in an ordered Banach spaces E. By introducing a new concept of lower and upper mild solutions, we construct a new monotone iterative method for the initial value problem of evolution equations with non-instantaneous imp...

We consider a class of fractional evolution equations with nonlocal integral conditions in Banach spaces. New existence of mild solutions to such a problem are established using Schauder fixed-point theorem, diagonal argument and approximation techniques under the hypotheses that the nonlinear term is Carathéodory continuous and satisfies some weak...

In this paper, we are concerned with the existence of mild solutions for the initial value problem to a new class of abstract evolution equations with non-instantaneous impulses on ordered Banach spaces. The existence and uniqueness theorem of mild solution for the associated linear evolution equation with non-instantaneous impulses is established....

This paper is concerned with the existence and uniqueness of global strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. We assume that the linear part is a positive definite selfadjoint operator, and the nonlinear part satisfies some essential growth conditions. The discussions are b...

The aim of this paper is to discuss the global existence, uniqueness and asymptotic stability of mild solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. A sufficient condition is given for judging the relative compactness of a class of abstract continuous family of functions on infinite in...

In this paper, we deal with a class of nonlinear time fractional non-autonomous evolution equations with delay by introducing the operators , and , which are generated by the operator and probability density function. The definition of mild solutions for studied problem was given based on these operators. Combining the techniques of fractional calc...

In this paper, we study the existence of solutions for a class of nonlinear higher-order fractional differential equation with fractional nonlocal boundary condition by using the monotone iterative technique based on the method of upper and lower solutions and give a specific iterative equation about its solutions.

In this article, we are concerned with a class of fractional stochastic evolution equations with nonlocal initial conditions in Hilbert spaces. The existence of mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using fractional calculations, Schauder fixed point theorem, stochasti...

In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth conditi...

In this article, we are concerned with the existence of extremal solutions to the initial value problem of impulsive differential equations in ordered Banach spaces. The existence and uniqueness theorem for the solution of the associated linear impulsive differential equation is established. With the aid of this theorem, the existence of minimal an...

This paper deals with the existence and uniqueness of time periodic solutions for the general periodic parabolic equation boundary problem with nonlocal delay. We apply operator semigroup theory and monotone iterative technique of lower and upper solutions to obtain the existence and uniqueness of o-periodic mild solutions of some abstract evolutio...

This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.

The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. The results obtained in this paper impr...

In this paper, we discuss the continuous dependence of mild solutions on initial values and orders for the initial value problem of fractional evolution equations in infinite dimensional spaces. The results obtained in this paper improve and extend some related conclusions on this topic. This paper can be considered as a contribution to this emergi...

The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. The results obtained in this paper impr...

We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We construct Green’s function for the associated linear boundary value pr...

In this paper we use a monotone iterative technique in the presence of the lower and upper solutions to discuss the existence of mild solutions for a class of semilinear impulsive integro-differential evolution equations of Volterra type with nonlocal conditions in a Banach space E where A: D(A) ⊂ E → E is a closed linear operator and −A generates...

This paper deals with the existence and uniqueness of positive mild solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The existence and uniqueness of mild solution for the associated linear evolution equation nonlocal problem is established, and the spectral radius of resolvent operator i...

This paper is concerned with the existence of -mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space. We assume that the linear part generates a compact, analytic and uniformly bounded semigroup, the nonlinear part satisfies some local growth c...

This paper deals with the existence and uniqueness of solutions of the fourth-order periodic boundary value problem { u ( 4 ) ( t ) = f ( t , u ( t ) , u ″ ( t ) ) , t ∈ [ 0 , 1 ] , u ( i ) ( 0 ) = u ( i ) ( 1 ) , i = 0 , 1 , 2 , 3 , where f : [ 0 , 1 ] × R × R → R is continuous. Under two-parameter nonresonance conditions described...

In this paper, we are concerned with nonlocal problem for fractional evolution equations with mixed monotone nonlocal term of the form $$\left\{\begin{array}{ll}^CD^{q}_tu(t) + Au(t) = f(t, u(t), u(t)),\quad t \in J = [0, a],\\u(0) = g(u, u),\end{array}\right.$$where E is an infinite-dimensional Banach space, \({^CD^{q}_t}\) is the Caputo fractiona...

This paper discusses the existence and uniqueness of mild solutions for a class of semilinear evolution equations with nonlocal conditions in an ordered Banach space E. Under some monotonicity conditions and noncompactness measure conditions of the nonlinearity, a new monotone iterative method on the evolution equations with nonlocal conditions has...

This paper deals with the existence of mild solutions for a class of semilinear nonlocal impulsive evolution equations in ordered Banach spaces. The existence and uniqueness theorem of a mild solution for the associated linear nonlocal impulsive evolution equation is established. With the aid of the theorem, the existence of mild solutions for nonl...

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theor...

A general class of semilinear fractional evolution equations of mixed type with nonlocal conditions on infinite dimensional Banach spaces is concerned. Under more general conditions, the existence of mild solutions and positive mild solutions is obtained by utilizing a new estimation technique of the measure of noncompactness and a new fixed point...

This paper discusses the existence of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions in Hilbert spaces. The discussion is based on analytic semigroups theory and fixed point theorem. An application to a partial differential equation with nonlocal condition is also considered. Mathematics Subject Cla...

This paper deals with the existence of mild L-quasi-solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established. The...

By employing the method of upper and lower solutions and the monotone iterative technique, the authors study a class of boundary value problems for first order impulsive differential equations with infinite skip points in Banach spaces. The existence of the maximal and minimal solutions are obtained under weak conditions.

This paper deals with the existence of L -quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Our result improves and extends some...

We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem $$displaylines{ u&apos;(t)+Au(t)= f(t,u(t),Tu(t)),quad tin J,; teq t_k,cr Delta u |_{t=t_k}=I_k(u(t_k)) ,quad k=1,2,dots ,m,cr u(0)=x_0, }$$ where $A:D(A)subset Eo E$ is a closed lin...