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2006 Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$
Claudianor O. Alves, Giovany M. Figueiredo
Differential Integral Equations 19(2): 143-162 (2006).

Abstract

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of problem \begin{equation} - \epsilon^{p} \Delta_{p}u + V(z)|u|^{p-2}u=f(u), \,\,\, u(z) > 0, \forall \ z \in \mathbb R^N , \tag*{$(P_{\epsilon})$} \end{equation} where $\Delta_{p}u$ is the p-Laplacian operator, $\epsilon$ is a positive parameter, $2 \leq p < N, V:\mathbb R^N \to \mathbb R$ is a continuous functions and $f:\mathbb R \to \mathbb R$ is a function of $C^{1}$ class.

Citation

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Claudianor O. Alves. Giovany M. Figueiredo. "Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$." Differential Integral Equations 19 (2) 143 - 162, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35107
MathSciNet: MR2194501

Subjects:
Primary: 35J60
Secondary: 35B25, 47J30, 58E05

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 2 • 2006
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