A continuation approach to fourth order superlinear periodic boundary value problems
type: Item
instance of: scholarly article
title: A continuation approach to fourth order superlinear periodic boundary value problems
zbMATH Open document ID: 0799.34024
DOI: 10.12775/TMNA.1993.030
author: Jean Mawhin
author: Fabio Zanolin
published in: Topological Methods in Nonlinear Analysis
publication date: 1994-11-13T00:00:00Z
review text: The purpose of this paper is to prove existence of \(T\)-periodic solutions of \(u''''= g(u)+e(t)\) in case \(g\) is a continuous function satisfying \(\lim_{| x|\to +\infty} g(x)/x =+\infty\) and \(e\) is continuous and \(T\)-periodic. The method of proof is based on degree theory and uses a continuation theorem developed in \textit{A. Capietto}, \textit{J. Mawhin} and \textit{F. Zanolin} [J. Differ. Equations 88, 347-395 (1990; Zbl 0718.34053)] in order to deal with problems in which there is no a priori bounds for the solutions.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 591505
zbMATH Keywords: periodic solutions
zbMATH Keywords: degree theory
zbMATH Keywords: continuation theorem
reviewed by: Patrick Habets
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 591505