# Nonlinear Differential Equations and Applications NoDEA (NODEA-NONLINEAR DIFF )

Publisher: Springer Verlag

## Description

The purpose of the Journal NoDEA - Nonlinear Differential Equations and Applications - is to encourage the interaction between pure mathematics and applied sciences. In particular it will provide a forum for research papers on nonlinear differential equations and applications to natural sciences. General theory will include ordinary and partial differential equations (both deterministic and stochastic) variational and topological methods control theory qualitative analysis including stability and bifurcation. Applications to natural sciences include the treatment of problems in classical statistical and quantum mechanics electromagnetism population dynamics chemical kinetics combustion theory.

• Impact factor
0.67
Show impact factor history

Impact factor
.
Year
• 5-year impact
0.92
• Cited half-life
5.70
• Immediacy index
0.11
• Eigenfactor
0.00
• Article influence
0.88
• Website
Nonlinear Differential Equations and Applications website
• Other titles
Nonlinear differential equations and applications (Online), NoDEA
• ISSN
1021-9722
• OCLC
43346736
• Material type
Document, Periodical, Internet resource
• Document type
Internet Resource, Computer File, Journal / Magazine / Newspaper

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author can archive a post-print version
• Conditions
• Authors own final version only can be archived
• Publisher's version/PDF cannot be used
• On author's website or institutional repository
• On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
• Published source must be acknowledged
• Must link to publisher version
• Set phrase to accompany link to published version (The original publication is available at www.springerlink.com)
• Articles in some journals can be made Open Access on payment of additional charge
• Classification
​ green

## Publications in this journal

• ##### Article: An approximation scheme for the anisotropic and nonlocal mean curvature flow
[Hide abstract]
ABSTRACT: In 2004 Chambolle proposed an algorithm for mean curvature flow based on a variational problem. Since then, the convergence, extensions and applications of his algorithm have been studied by many people. In this paper we give a proof of the convergence of an anisotropic version of Chambolle’s algorithm by use of the signed distance function. An application of our scheme to an approximation of the nonlocal curvature flow such as crystalline one is also discussed.
Nonlinear Differential Equations and Applications NoDEA 04/2014; 21(2).
• ##### Article: Infinite speed of support propagation for the Derrida–Lebowitz–Speer–Spohn equation and quantum drift–diffusion models
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ABSTRACT: We show that weak solutions of the Derrida–Lebowitz–Speer–Spohn (DLSS) equation display infinite speed of support propagation. We apply our method to the case of the quantum drift–diffusion equation which augments the DLSS equation with a drift term and possibly a second-order diffusion term. The proof is accomplished using weighted entropy estimates, Hardy’s inequality and a family of singular weight functions to derive a differential inequality; the differential inequality shows exponential growth of the weighted entropy, with the growth constant blowing up very fast as the singularity of the weight becomes sharper. To the best of our knowledge, this is the first example of a nonnegativity-preserving higher-order parabolic equation displaying infinite speed of support propagation.
Nonlinear Differential Equations and Applications NoDEA 02/2014;
• ##### Article: An Osgood type regularity criterion for the liquid crystal flows
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ABSTRACT: In this paper, we prove an Osgood type regularity criterion for the model of liquid crystals, which says that the condition implies the smoothness of the solution. Here, [TEX equation: {{\bar S_q=\sum\nolimits_{k=-q}^q \dot {\triangle}_k}}] with [TEX equation: {\dot{\triangle}_k}] being the frequency localization operator.
Nonlinear Differential Equations and Applications NoDEA 01/2014; 21(2).
• ##### Article: Wellposedness in the Lipschitz class for a quasi-linear hyperbolic system arising from a model of the atmosphere including water phase transitions
Nonlinear Differential Equations and Applications NoDEA 01/2014;
• ##### Article: The Mather problem for lower semicontinuous Lagrangians
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ABSTRACT: In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler–Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity.
Nonlinear Differential Equations and Applications NoDEA 01/2014;
• ##### Article: {W^{1,1}_0} -solutions for elliptic problems having gradient quadratic lower order terms
[Hide abstract]
ABSTRACT: In this paper we deal with solutions of problems of the type $$\left\{\begin{array}{ll}-{\rm div} \Big(\frac{a(x)Du}{(1+|u|)^2} \Big)+u = \frac{b(x)|Du|^2}{(1+|u|)^3} +f \quad &{\rm in} \, \Omega,\\ u=0 &{\rm on} \partial \, \Omega, \end{array} \right.$$ where ${0 < \alpha \leq a(x) \leq \beta, |b(x)| \leq \gamma, \gamma > 0, f \in L^2 (\Omega)}$ and Ω is a bounded subset of ${\mathbb{R}^N}$ with N ≥ 3. We prove the existence of at least one solution for such a problem in the space ${W_{0}^{1, 1}(\Omega) \cap L^{2}(\Omega)}$ if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: $$J (v) = \frac{\alpha}{2} \int_{\Omega}\frac{|D v|^2}{(1 + |v|)^{2}} + \frac{12}{\int_{\Omega}|v|^2} - \int_{\Omega}f\,v , \quad f \in L^2(\Omega),$$ where in this case a(x) ≡ b(x) = α > 0.
Nonlinear Differential Equations and Applications NoDEA 12/2013;
• Source
##### Article: Symplectic and contact properties of the Ma\~n\'e critical value of the universal cover
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ABSTRACT: We discuss several symplectic aspects related to the Ma\~n\'e critical value c_u of the universal cover of a Tonelli Hamiltonian. In particular we show that the critical energy level is never of virtual contact type for manifolds of dimension greater than or equal to three. We also show the symplectic invariance of the finiteness of the Peierls barrier and the Aubry set of the universal cover. We also provide an example where c_u coincides with the infimum of Mather's \alpha -function but the Aubry set of the universal cover is empty and the Peierls barrier is finite. A second example exhibits all the ergodic invariant minimizing measures with zero homotopy, showing that the union of their supports is not a graph, in contrast with Mather's celebrated graph theorem.
Nonlinear Differential Equations and Applications NoDEA 09/2013;
• ##### Article: A remark on the existence of slowly growing positive solutions to second order super-linear ordinary differential equations
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ABSTRACT: In this paper second order super-linear ordinary differential equations are considered, and a sufficient condition for the existence of a slowly growing positive solution is given.
Nonlinear Differential Equations and Applications NoDEA 01/2013;
• ##### Article: Brownian motion and exposed solutions of differential inclusions
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ABSTRACT: We present a research program designed by A. Bressan and some partial results related to it. First, we construct a probability measure supported on the space of solutions to a planar differential inclusion, where the right-hand side is a Lipschitz continuous segment. Such measure assigns probability one to solutions having derivatives a.e. equal to one of the endpoints of the segment. Second, for a class of planar differential inclusions with Hölder continuous right-hand side F, we prove existence of solutions whose derivatives are exposed points of F. Finally, we complete the research program if the right-hand side of the differential inclusion does not depend on the state and prove a result on the Lipschitz continuity of an auxiliary map. The proofs rely on basic properties of Brownian motion.
Nonlinear Differential Equations and Applications NoDEA 01/2013; 20(2).
• ##### Article: On the existence of periodic and homoclinic orbits for first order superquadratic Hamiltonian systems
[Hide abstract]
ABSTRACT: In this paper we consider the following Hamiltonian system $$J\dot u + B(t)u +\nabla W(t,u)=0.\quad\quad (HS)$$ Under a new superquadratic assumption on the potential, we prove that (HS) has a sequence of subharmonics. This will be done using a minimax result in critical point theory. Also, we study the asymptotic behavior of these subharmonics and we establish the existence of a homoclinic orbit for (HS). Previous results in the topic, mainly those due to Rabinowitz and Tanaka, are significantly improved.
Nonlinear Differential Equations and Applications NoDEA 01/2013; 20(3).
• ##### Article: On the stochastic 2-D motion of a Bingham fluid
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ABSTRACT: We establish the existence and uniqueness of a strong solution to the initial boundary value problem associated with the motion of a Bingham fluid in a two-dimensional domain with random noise. We also prove the existence of an invariant measure for a certain class of noise. When the deterministic forcing is sufficiently small and the multiplicative noise is almost linear, it is shown that extinction of a solution occurs in a finite time almost surely.
Nonlinear Differential Equations and Applications NoDEA 01/2013; 20(3).
• ##### Article: Extended quasi-homogeneous polynomial system in {\mathbb{R}^{3}}
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ABSTRACT: In this paper we define an extended quasi-homogeneous polynomial system d x/dt = Q = Q 1 + Q 2 + ... + Q δ , where Q i are some 3-dimensional quasi-homogeneous vectors with weight α and degree i, i = 1, . . . ,δ. Firstly we investigate the limit set of trajectory of this system. Secondly let Q T be the projective vector field of Q. We show that if δ ≤ 3 and the number of closed orbits of Q T is known, then an upper bound for the number of isolated closed orbits of the system is obtained. Moreover this upper bound is sharp for δ = 3. As an application, we show that a 3-dimensional polynomial system of degree 3 (resp. 5) admits 26 (resp. 112) isolated closed orbits. Finally, we prove that a 3-dimensional Lotka-Volterra system has no isolated closed orbits in the first octant if it is extended quasi-homogeneous.
Nonlinear Differential Equations and Applications NoDEA 01/2013;
• ##### Article: Nonlinear diffusion equations driven by the p(·)-Laplacian
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ABSTRACT: This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole or in a subset of the domain. To this end, the recent developments in the studies of variable exponent Lebesgue and Sobolev spaces are exploited, and moreover, the spatial inhomogeneity of variable exponents p(·) is appropriately controlled to obtain each result.
Nonlinear Differential Equations and Applications NoDEA 01/2013; 20(1).
• ##### Article: p-Laplacian problems with nonlinearities interacting with the spectrum
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ABSTRACT: The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problem $$\left\{\begin{array}{ll}-\Delta_p u\ =\ g(x, u) \quad {\rm in} \quad \Omega,\\ u=0 \qquad \qquad \qquad {\rm on}\quad \partial\Omega,\end{array}\right.$$ where ${1 < p < + \infty, \Delta_p u = {\rm div}(|\nabla {u}|^{p-2}\nabla {u})}$ , Ω is an open bounded domain of ${\mathbb{R}^N (N \geq 3)}$ with smooth boundary ∂Ω and the nonlinearity g behaves as u p−1 at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981–1012, 1983), but extended to Banach spaces, and two sequences of quasi–eigenvalues for the p–Laplacian operator as in Candela and Palmieri (Calc. Var. 34: 495–530, 2009), Li and Zhou (J. Lond. Math. Soc. 65: 123–138, 2002).
Nonlinear Differential Equations and Applications NoDEA 01/2013;
• ##### Article: Multiple positive solutions of singular and critical elliptic problem in {\mathbb{R}^2} with discontinuous nonlinearities
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ABSTRACT: Let Ω be a bounded domain in ${\mathbb{R}^2}$ with smooth boundary. We consider the following singular and critical elliptic problem with discontinuous nonlinearity: $$(P_\lambda)\left \{\begin{array}{ll} - \Delta u = \lambda \left(\frac{m(x, u) e^{\alpha{u}^2}}{|x|^{\beta}} + u^{q}g(u - a)\right),\quad{u} > 0 \quad {\rm in} \quad \Omega\\u \quad \quad = 0\quad {\rm on} \quad \partial \Omega \end{array}\right.$$ where ${0\leq q < 1 ,0< \alpha\leq4\pi}$ and ${\beta \in [0, 2)}$ such that ${\frac{\beta}{2} + \frac{\alpha}{4\pi} \leq 1}$ and ${{g(t - a) = \left\{\begin{array}{ll}1, t \leq a\\ 0, t > a.\end{array}\right.}}$ Under the suitable assumptions on m(x, t) we show the existence and multiplicity of solutions for maximal interval for λ.
Nonlinear Differential Equations and Applications NoDEA 01/2013;

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