Multiple solutions for a problem with resonance involving thep-Laplacian-Reference-Cited by-同舟云学术

Multiple solutions for a problem with resonance involving thep-Laplacian

Published:1998 Issue:1-2 Volume:3 Page:191-201
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Alves C. O.¹,Carrião P. C.²,Miyagaki O. H.³

Affiliation:

1. Departamento de matemática e Estatística, Universidade Federal da Paraíba, Campina Grande 58109-970, (PB), Brazil

2. Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte 31270-010, (MG), Brazil

3. Departamento de Matemática, Universidade Federal de Viçosa, Viçosa 36571-000, (MG), Brazil

Abstract

In this paper we will investigate the existence of multiple solutions for the problem(P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω)whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator,Ω⫅ℝNis a bounded domain with smooth boundary,handgare bounded functions,N≥1and1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/1998/315492.pdf

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