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A result of multiplicity of solutions for a class of quasilinear equations

Part of: Equations of mathematical physics and other areas of application Close-to-elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  23 February 2012

Claudianor O. Alves ,
Giovany M. Figueiredo  and
Uberlandio B. Severo
Claudianor O. Alves
Affiliation:
Unidade Acadêmica de Matemática e Estatística, Universidade Federal de Campina Grande, 58109-970 Campina Grande PB, Brazil (coalves@dme.ufcg.edu.br)
Giovany M. Figueiredo
Affiliation:
Unidade Acadêmica de Matemática e Estatística, Universidade Federal de Campina Grande, 58109-970 Campina Grande PB, Brazil (coalves@dme.ufcg.edu.br) Faculdade de Matemática, Universidade Federal do Pará, 66075-110 Belém PA, Brazil (giovany@ufpa.br)
Uberlandio B. Severo
Affiliation:
Departamento de Matemática, Universidade Federal da Paraíba, 58051-900 João Pessoa PB, Brazil (uberlandio@mat.ufpb.br)
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Abstract

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We establish the multiplicity of positive weak solutions for the quasilinear Dirichlet problem −Lpu + |u|p−2u = h(u) in Ωλ, u = 0 on ∂Ωλ, where Ωλ = λΩ, Ω is a bounded domain in ℝN, λ is a positive parameter, Lpu ≐ Δpu + Δp(u2)u and the nonlinear term h(u) has subcritical growth. We use minimax methods together with the Lyusternik–Schnirelmann category theory to get multiplicity of positive solutions.

Keywords

variational methodsquasilinear equationsstanding wave solutionsLyusternik–Schnirelmann category

MSC classification

Secondary: 35A15: Variational methods 35H30: Quasi-elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 291 - 309
Copyright
Copyright © Edinburgh Mathematical Society 2012

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