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November/December 2010 Multiplicity of positive solutions for a class of nonlinear Schrödinger equations
Claudianor O. Alves, Sérgio H. M. Soares
Adv. Differential Equations 15(11/12): 1083-1102 (November/December 2010).

Abstract

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: $$ \begin{cases} -\epsilon^{p}\Delta_{p}{u}+(\lambda A(x)+1)|u|^{p-2}u=f(u), \,\,\, \mathbb{R}^{N}\\ u(x)>0 \,\,\, \mbox{in} \,\, \mathbb{R}^{N}, \end{cases} $$ where $\Delta_{p}$ is the p-Laplacian operator, $ N >p \geq 2$, $\lambda$ and $\epsilon$ are positive parameters, $A$ is a nonnegative continuous function and $f$ is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of ${\rm{int}}A^{-1}(0)$ for all sufficiently large $\lambda$ and small~$\epsilon$.

Citation

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Claudianor O. Alves. Sérgio H. M. Soares. "Multiplicity of positive solutions for a class of nonlinear Schrödinger equations." Adv. Differential Equations 15 (11/12) 1083 - 1102, November/December 2010.

Information

Published: November/December 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1219.35115
MathSciNet: MR2743495

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Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.15 • No. 11/12 • November/December 2010
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