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2004 Multiple positive solutions for classes of $p$-Laplacian equations
Mythily Ramaswamy, Ratnasingham Shivaji
Differential Integral Equations 17(11-12): 1255-1261 (2004).

Abstract

We study positive $C^1(\bar{\Omega})$ solutions to classes of boundary-value problems of the form \begin{eqnarray*} -\Delta_p u & = & \lambda f(u)\mbox{ in } \Omega \\ u & = & 0 \mbox{ on } \partial \Omega , \end{eqnarray*} where $ \Delta_{p} $ denotes the p-Laplacian operator defined by $$ \Delta_p z:= \mbox{div}(|\nabla z|^{p-2}\nabla z);\, p > 1,\, \lambda > 0 $$ is a parameter and $ \Omega $ is a bounded domain in $ R^{N} $; $ N \geq 2 $ with $\partial \Omega$ of class $ C^{2}$ and connected. (If $N=1$, we assume that $\Omega$ is a bounded open interval.) In particular, we establish existence of three positive solutions for classes of nondecreasing, p-sublinear functions $f$ belonging to $C^1([0,\infty))$. Our proofs are based on sub-supersolution techniques.

Citation

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Mythily Ramaswamy. Ratnasingham Shivaji. "Multiple positive solutions for classes of $p$-Laplacian equations." Differential Integral Equations 17 (11-12) 1255 - 1261, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.35419
MathSciNet: MR2100025

Subjects:
Primary: 35J60

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 11-12 • 2004
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