Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term
type: Item
instance of: scholarly article
title: Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term
zbMATH Open document ID: 1201.34104
published in: Applied Mathematics and Computation
publication date: 2010-06-25T00:00:00Z
review text: By using Lu's continuation theorem, which is an extension of a result of Manásevich-Mawhin, the authors study the existence of periodic solutions for the Rayleigh type \(p\)-Laplacian equation \[ (\varphi _p(x^{\prime}(t)))^{\prime}+f(x^{\prime}(t))+g_{1}(x(t-\tau _{1}(t,|x|_{\infty })))+\beta (t)g_{2}(x(t-\tau _{2}(t,|x|_{\infty })))=e(t). \] This paper includes the case that the growth order with respect to the variable \(u\) in \(g_1(u)\) is allowed to be greater than \(p-1\) and the coefficient \(\beta (t)\) of \(g_2(x(t-\tau _2(t, |x|_{\infty })))\) can change sign.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5726768
zbMATH Keywords: degree theory
zbMATH Keywords: periodic solution
zbMATH Keywords: \(p\)-Laplacian
author: Fabao Gao
author: Shiping Lu
author: Wei Zhang
reviewed by: Changpin Li
MaRDI profile type: Publication
full work available at URL: j.amc.2010.03.031
OpenAlex ID: W1973460986
cites work: Periodic solutions for second order differential inclusions with the scalar \(p\)-Laplacian
cites work: Multiple nontrivial solutions for nonlinear periodic problems with the \(p\)-Laplacian
cites work: Periodic solutions for \(p\)-Laplacian Rayleigh equations
cites work: Periodic solutions for a Rayleigh type equation with a variable coefficient ahead of the nonlinear term
cites work: Existence of periodic solutions for a Liénard type \(p\)-Laplacian differential equation with a deviating argument
cites work: New results of periodic solutions for Rayleigh type \(p\)-Laplacian equation with a variable coefficient ahead of the nonlinear term
cites work: Periodic solutions to a second order \(p\)-Laplacian neutral functional differential system
cites work: Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument
cites work: On the existence of periodic solutions to \(p\)-Laplacian Rayleigh differential equation with a delay
cites work: Periodic solution for nonlinear systems with \(p\)-Laplacian-like operators
cites work: Nonuniform nonresonance at the first eigenvalue of the p-laplacian
cites work: Periodic solutions for \(p\)-Laplacian neutral functional differential equation with multiple deviating arguments
DOI: 10.1016/J.AMC.2010.03.031
description: scientific article; zbMATH DE number 5726768