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2004 Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities
Norimichi Hirano, Claudio Saccon, Naoki Shioji
Adv. Differential Equations 9(1-2): 197-220 (2004). DOI: 10.57262/ade/1355867973

Abstract

We study the existence of multiple positive solutions of $ -\Delta u = \lambda u^{-q} +u^p $ in $\Omega$ with homogeneous Dirichlet boundary condition, where $\Omega$ is a bounded domain in $\mathbb R^N$, $\lambda >0$, and $0 < q \leq 1 < p \leq (N+2)/(N-2)$. We show by a variational method that if $\lambda$ is less than some positive constant then the problem has at least two positive, weak solutions including the cases of $q=1$ or $p=(N+2)/(N-2)$. We also study the regularity of positive weak solutions.

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Norimichi Hirano. Claudio Saccon. Naoki Shioji. "Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities." Adv. Differential Equations 9 (1-2) 197 - 220, 2004. https://doi.org/10.57262/ade/1355867973

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 05054519
MathSciNet: MR2099611
Digital Object Identifier: 10.57262/ade/1355867973

Subjects:
Primary: 35J65
Secondary: 35B65 , 35J20 , 47J30

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 1-2 • 2004
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