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September/October 2009 Multiplicity of positive solutions for a class of quasilinear problems
Claudianor O. Alves, Giovany M. Figueiredo, Uberlandio B. Severo
Adv. Differential Equations 14(9/10): 911-942 (September/October 2009).

Abstract

In this paper we prove the existence and multiplicity of nontrivial weak solutions for quasilinear elliptic equations of the form $-L_p u +V(x)|u|^{p-2}u= h(u)$ in $\mathbb{R}^N$, where $L_p u\doteq \epsilon^{p}\Delta_p u +\epsilon^{p}\Delta_p (u^2)u$ and $V$ is a positive continuous potential bounded away from zero satisfying some conditions and the nonlinear term $h(u)$ has a subcritical growth type. Here, we use a variational method to get the multiplicity of positive solutions involving the Lusternick-Schnirelman category of the set where $V$ achieves its minimum value.

Citation

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Claudianor O. Alves. Giovany M. Figueiredo. Uberlandio B. Severo. "Multiplicity of positive solutions for a class of quasilinear problems." Adv. Differential Equations 14 (9/10) 911 - 942, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1190.35099
MathSciNet: MR2548282

Subjects:
Primary: 35A15, 35H30, 35Q55

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 9/10 • September/October 2009
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