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2005 Existence results for a class of $p$-Laplacian problems with sign-changing weight
Maya Chhetri, Shobha Oruganti, R. Shivaji
Differential Integral Equations 18(9): 991-996 (2005).

Abstract

Consider the boundary-value problem \begin{equation} \begin{array}{c} -\Delta_p u = \lambda g(x)f(u) \quad \mbox{in}\ \Omega \nonumber\\ u=0 \quad \mbox{on}\quad \partial \Omega, \nonumber \end{array} \end{equation} where $\lambda > 0$ is a parameter, $\Omega$ is a bounded domain in $\mathbb R^N,\, N \geq 1,$ with sufficiently smooth boundary $\partial \Omega$ and $\Delta_p u:= div(|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for $p > 1$. Here $g$ is a $C^1$ sign-changing function that may be negative near the boundary and $f $ is a $C^1$ nondecreasing function satisfying $f(0)>0$. We discuss existence results for positive solutions when $f$ satisfies certain additional conditions. We employ the method of sub-super solutions to obtain our results.

Citation

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Maya Chhetri. Shobha Oruganti. R. Shivaji. "Existence results for a class of $p$-Laplacian problems with sign-changing weight." Differential Integral Equations 18 (9) 991 - 996, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35147
MathSciNet: MR2162422

Subjects:
Primary: 35J60
Secondary: 35J25

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 9 • 2005
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