A bifurcation result for a Dirichlet problem with discontinuous nonlinearity
type: Item
instance of: scholarly article
title: A bifurcation result for a Dirichlet problem with discontinuous nonlinearity
zbMATH Open document ID: 0703.35068
DOI: 10.1007/BF02844002
author: Daniela Lupo
publication date: 1989-01-01T00:00:00Z
review text: The author uses multivalued mapping and degree techniques to study the problem \[ -\Delta u=h(u-\alpha)p(u)\text{ in } \Omega;\quad u=0\text{ on } \partial \Omega. \] Here \(h(t)=0\) if \(t\leq 0\) and is one otherwise (and thus is discontinuous). She constructs generalized solutions. It is not clear whether the solution satisfies the equations almost everywhere because it is possible the solution equals \(\alpha\) on a set of positive measure. This problem has also been studied by \textit{A. Ambrosetti} and \textit{R. E. L. Turner} [Differ. Integr. Equations 1, 341-349 (1988)] by non-classical variational methods. Their method has the advantage that they can show some of the solutions satisfy the equation almost everywhere.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 4152993
zbMATH Keywords: degree
reviewed by: E. N. Dancer
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4152993