Hostname: page-component-7b9c58cd5d-dlb68 Total loading time: 0 Render date: 2025-03-15T19:38:03.916Z Has data issue: false hasContentIssue false

Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p-Laplacian

Published online by Cambridge University Press:  12 July 2007

Giovanni Anello
Affiliation:
Department of Mathematics, University of Messina, 98166 Sant' Agata-Messina, Italy (anello@dipmat.unime.it)
Giuseppe Cordaro
Affiliation:
Department of Mathematics, University of Messina, 98166 Sant' Agata-Messina, Italy (cordaro@dipmat.unime.it)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present a result of existence of infinitely many arbitrarily small positive solutions to the following Dirichlet problem involving the p-Laplacian, where Ω ∈ RN is a bounded open set with sufficiently smooth boundary ∂Ω, p > 1, λ > 0, and f: Ω × R → R is a Carathéodory function satisfying the following condition: there exists > 0 such that Precisely, our result ensures the existence of a sequence of a.e. positive weak solutions to the above problem, converging to zero in L(Ω).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2002