Multiple solutions for a problem with resonance involving the p -Laplacian

C. O. Alves, P. C. Carrião and O. H. Miyagaki

Abstract and Applied Analysis, 1998, vol. 3, 1-11

Abstract:

In this paper we will investigate the existence of multiple solutions for the problem ( P ) − Δ p u + g ( x , u ) = λ 1 h ( x ) | u | p − 2 u , in Ω , u ∈ H 0 1 , p ( Ω ) where Δ p u = div ( | ∇ u | p − 2 ∇ u ) is the p -Laplacian operator, Ω ⫅ ℝ N is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 < p < ∞ . Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:315492

DOI: 10.1155/S1085337598000517

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