Existence of periodic solutions for quasilinear differential equations
type: Item
instance of: scholarly article
title: Existence of periodic solutions for quasilinear differential equations
zbMATH Open document ID: 1057.34037
DOI: 10.1016/S0096-3003(03)00627-1
author: Xiaojing Yang
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The paper deals with the nonlinear differential equation with \(p\)-Laplacian \[ ( \phi_{p}( u^{\prime}) ) ^{\prime}+f(t,u,u^{\prime })=0, \] where \(\phi_{p}(u)=| u| ^{p-2}u,\) \(p>1\) and \(f:[0,T]\times \mathbb{R}^{2}\to\mathbb{R}\) is a continuous, \(T\)-periodic function in \(t\) for some \(T>0.\) Using a fixed-point theorem due to \textit{T. Ding} [Chin. Ann. Math. 2, 281--300 (1981; Zbl 0484.34025)], the author obtains new sufficient conditions for the existence of \(T\)-periodic solutions. The paper concludes with an illustrative example. It should be noted that during the last decade there has been an increasing interest in the study of differential equations with \(p\)-Laplacian, and many papers on the subject have been published. Unfortunately, the bibliography contains only three items with the most recent paper dated 1992.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2081731
zbMATH Keywords: periodic solutions
zbMATH Keywords: existence
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: differential equation
zbMATH Keywords: fixed-point theorem
reviewed by: Svitlana P. Rogovchenko
MaRDI profile type: Publication
cites work: Existence and multiplicity of solutions with prescribed period for a second order quasilinear O.D.E.
cites work: Q3943259
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
full work available at URL: s0096-3003(03)00627-1
OpenAlex ID: W2060497483
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description: scientific article; zbMATH DE number 2081731