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2010 Existence of Positive Bounded Solutions of Semilinear Elliptic Problems
Faten Toumi
Int. J. Differ. Equ. 2010: 1-10 (2010). DOI: 10.1155/2010/134078

Abstract

This paper is concerned with the existence of bounded positive solution for the semilinear elliptic problem Δu=λp(x)f(u) in Ω subject to some Dirichlet conditions, where Ω is a regular domain in n(n3) with compact boundary. The nonlinearity f is nonnegative continuous and the potential p belongs to some Kato class K(Ω). So we prove the existence of a positive continuous solution depending on λ by the use of a potential theory approach.

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Faten Toumi. "Existence of Positive Bounded Solutions of Semilinear Elliptic Problems." Int. J. Differ. Equ. 2010 1 - 10, 2010. https://doi.org/10.1155/2010/134078

Information

Received: 18 June 2010; Accepted: 25 September 2010; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1221.35160
MathSciNet: MR2746095
Digital Object Identifier: 10.1155/2010/134078

Rights: Copyright © 2010 Hindawi

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