Multiple positive solutions for nonlinear periodic problems
type: Item
instance of: scholarly article
title: Multiple positive solutions for nonlinear periodic problems
zbMATH Open document ID: 1209.34029
author: Shouchuan Hu
author: Nikolaos S. Papageorgiou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-11-19T00:00:00Z
review text: The authors discuss the existence and the multiplicity of positive solutions to the following \(p\)-Laplacian periodic problem: \[ \begin{cases} -(| x'(t)|^{p-2}x'(t))'=f(t,x(t)), \quad 0<t<b,\\ x(0=x(b),\quad x'(0)=x'(b), \end{cases} \] where the nonlinearity \(f\) is a \((p-1)\)-Carathéodory function with super-linear growth at the space-origin. Using variational methods involving the Cerami condition, the authors prove the existence of at least two positive solutions. In the particular case of the semi-linear problem (\(p=2\)), the existence of three distinct positive solutions is obtained using Morse theory.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5817643
zbMATH Keywords: periodic scalar \(p\)-Laplacian
zbMATH Keywords: mountain pass theorem
zbMATH Keywords: Morse theory
reviewed by: Smail Djebali
MaRDI profile type: Publication
full work available at URL: j.na.2010.06.056
OpenAlex ID: W2055222235
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DOI: 10.1016/J.NA.2010.06.056
description: scientific article; zbMATH DE number 5817643