Existence of nonconstant periodic solutions for a class of second-order systems with \(p(t)\)-Laplacian
type: Item
instance of: scholarly article
title: Existence of nonconstant periodic solutions for a class of second-order systems with \(p(t)\)-Laplacian
zbMATH Open document ID: 1384.34047
author: Yukun An
author: Yuanfang Ru
author: Fanglei Wang
published in: Boundary Value Problems
publication date: 2018-01-17T00:00:00Z
review text: This article deals with the existence of periodic solutions for the \(p(t)\)-Laplacian system \[ (|u'(t)|^{p(t)-2}u'(t))' +\nabla F(t, u) =0, t\in [0, T], \] \[ u(0)-u(T) = u'(0)-u'(T) =0, \] where \(T>0\), \(u\in \mathbb{R}^N\), \(F: [0, T]\times \mathbb{R}^N \to \mathbb{R}\) and \(p(t)\) is a positive continuous \(T\)-periodic function. Under certain assumptions, it is shown that the system has at least one nonconstant \(T\)-periodic solution. Similar results can be found in the literature. It shows that the result obtained here covers some known results as particular cases, thus it extends the existing theories for the system.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 6826944
zbMATH Keywords: \(p(t)\)-Laplacian
zbMATH Keywords: second order differential equations
zbMATH Keywords: periodic solution
Wikidata QID: Q59527492
MaRDI profile type: Publication
full work available at URL: s13661-017-0901-y
OpenAlex ID: W2770384187
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DOI: 10.1186/S13661-017-0901-Y
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description: scientific article; zbMATH DE number 6826944