Periodic solutions for a differential inclusion problem involving the \(p(t)\)-Laplacian
type: Item
instance of: scholarly article
title: Periodic solutions for a differential inclusion problem involving the \(p(t)\)-Laplacian
zbMATH Open document ID: 1471.34043
author: Peng Chen
author: X. H. Tang
published in: Advances in Nonlinear Analysis
publication date: 2021-06-24T00:00:00Z
review text: The paper studies the periodic problem \[ -(|u'(t)|^{p(t)-2}u'(t))'\in \partial j(t,u(t))\quad a.e.\; t\in [0,T],\quad u(0)=u(T),\; u'(0)=u'(T), \] where \(p(.):[0,T]\to \mathbb{R}\) is continuous, \(p(t+T)=p(t)\) \(\forall t\in \mathbb{R}\), \(p(t)>1\) \(\forall t\in \mathbb{R}\), \(j(.,.):[0,T]\times {\mathbb{R}}^N\to \mathbb{R}\) is locally Lipschitz in the second variable and \(\partial j(t, .)\) denotes the subdifferential in the sense of Clarke. Under certain technical assumptions on the function \(j(.,.)\) the authors prove five results concerning the existence of a nontrivial solution of the problem considered.
reviewed by: Aurelian Cernea
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 7363135
zbMATH Keywords: locally Lipschitz
zbMATH Keywords: periodic solution
zbMATH Keywords: \(p(t)\)-Laplacian
zbMATH Keywords: nonsmooth critical point theory
MaRDI profile type: Publication
full work available at URL: anona-2020-0156
OpenAlex ID: W3117999351
cites work: A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions
cites work: On stationary thermo-rheological viscous flows
cites work: Variational methods for non-differentiable functionals and their applications to partial differential equations
cites work: Variable Exponent, Linear Growth Functionals in Image Restoration
cites work: Q4000274
cites work: Infinitely many solutions for a Neumann-type differential inclusion problem involving the \(p(x)\)-Laplacian
cites work: Infinitely many solutions for a hemivariational inequality involving the \(p(x)\)-Laplacian
cites work: Three solutions for a Neumann-type differential inclusion problem involving the \(p(x)\)-Laplacian
cites work: Infinitely many solutions for a differential inclusion problem in \(\mathbb R^N\) involving the \(p(x)\)-Laplacian
cites work: Existence and uniqueness results for some nonlinear boundary value problems
cites work: Existence and multiplicity of solutions with prescribed period for a second order quasilinear O.D.E.
cites work: Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent
cites work: A Knobloch-type result for \(p(t\))-Laplacian systems.
cites work: On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
cites work: Existence and multiplicity results for nonlinear nonautonomous second-order systems
cites work: On the existence of positive solutions for hemivariational inequalities driven by the \(p\)-Laplacian
cites work: ON THE EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS FOR EQUATIONS DRIVEN BY THE $p$-LAPLACIAN AND WITH A NON-SMOOTH POTENTIAL
cites work: Existence and multiplicity of solutions for second order periodic systems with the \(p\)-Laplacian and a nonsmooth potential
cites work: Solutions and multiple solutions for problems with the \(p\)-Laplacian
cites work: Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities
cites work: Q4761442
cites work: Critical point theory and Hamiltonian systems
cites work: Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the \(p\)-Laplacian
cites work: Two nontrivial solutions for quasilinear periodic equations
cites work: Handbook of applied analysis
cites work: Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems
cites work: Three nontrivial solutions for the \(p\)-Laplacian with a nonsmooth potential
cites work: Periodic solutions for a class of evolution inclusions
cites work: Nonlinear second-order periodic systems with non-smooth potential
cites work: Existence of solutions for \(p(x)\)-Laplacian nonhomogeneous Neumann problems with indefinite weight
cites work: Nonlinear elliptic equations with variable exponent: old and new
cites work: On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
cites work: Periodic solutions for second order systems with not uniformly coercive potential
cites work: Existence and subharmonicity of solutions for nonlinear non-smooth periodic systems with a \(p\)-Laplacian
cites work: Existence of periodic solutions for \(p(t)\)-Laplacian systems
cites work: Multiple periodic solutions of a class of \(p\)-Laplacian
cites work: Existence of radial solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
cites work: Q4308736
cites work: On some variational problems
cites work: AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
DOI: 10.1515/ANONA-2020-0156
Recommended article: Existence of periodic solutions for a differential inclusion system involving the \(p(t)\)-Laplacian
Recommended article: Periodic solutions of second-order differential inclusions systems with \(p(t)\)-Laplacian
Recommended article: Q4955275
Recommended article: Q5490088
Recommended article: On the existence of periodic solutions for differential inclusions
Recommended article: Q4296502
Recommended article: Periodic solutions of differential inclusions
Recommended article: Periodic solutions of second-order differential inclusions systems with \(p\)-Laplacian
Recommended article: On the periodic solutions of differential inclusions and applications
Recommended article: Q4434617
description: scientific article; zbMATH DE number 7363135