Existence and subharmonicity of solutions for nonlinear non-smooth periodic systems with a \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Existence and subharmonicity of solutions for nonlinear non-smooth periodic systems with a \(p\)-Laplacian
zbMATH Open document ID: 1146.34036
author: Kaimin Teng
author: Xian Wu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-06-10T00:00:00Z
review text: The authors prove the existence of periodic solutions to systems of ODE's involving a differential operator of \(p\)-Laplacian-type. In order to do this, they use variational methods. More precisely, since the nonlinearity is not assumed to be smooth, they need to use nonsmooth critical point theory. In this situation, they are also able to prove the existence of subharmonic solutions.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 5285999
zbMATH Keywords: locally Lipschitz
zbMATH Keywords: periodic solutions
zbMATH Keywords: subharmonic solutions
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Poincaré-Wirtinger inequality
reviewed by: Alessandro Fonda
MaRDI profile type: Publication
full work available at URL: j.na.2007.04.016
OpenAlex ID: W2078380268
cites work: Variational methods for non-differentiable functionals and their applications to partial differential equations
cites work: Optimization and nonsmooth analysis
cites work: Q4815703
cites work: Positive solutions and multiple solutions for periodic problems driven by scalarp -Laplacian
cites work: Q4761442
cites work: Two nontrivial critical points for nonsmooth functionals via local linking and applications
cites work: Critical point theory for nonsmooth functionals
cites work: On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems
cites work: Critical point theory and Hamiltonian systems
cites work: Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems
cites work: Nonlinear second-order periodic systems with non-smooth potential
cites work: On subharmonic solutions of hamiltonian systems
cites work: On a Class of Functionals Invariant under a Z n Action
cites work: Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations
cites work: Periodic solutions of non-autonomous second order systems
cites work: Existence and multiplicity of periodic solutions for nonautonomous second order systems
cites work: Periodic solutions for nonautonomous second order systems with sublinear nonlinearity
cites work: Periodic solutions of non-autonomous second order systems with \(\gamma\)- quasisubadditive potential
cites work: Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems
cites work: Periodic and subharmonic solutions of second-order Hamiltonian systems
cites work: Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems
cites work: Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors
cites work: Periodic solutions for a class of nonautonomous second-order systems
cites work: Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity
cites work: Saddle point reduction method for some non-autonomous second order systems
DOI: 10.1016/J.NA.2007.04.016
description: scientific article; zbMATH DE number 5285999