Robin problems involving the p(x)-Laplacian

Mostafa Allaoui

Applied Mathematics and Computation, 2018, vol. 332, issue C, 457-468

Abstract: By applying Mountain Pass Lemma and Ekeland’s variational principle, we prove two different situations of the existence of solutions for the following Robin problem −Δp(x)u=λV(x)|u|q(x)−2uinΩ,|∇u|p(x)−2∂u∂ν+β(x)|u|p(x)−2u=0on∂Ω,where Ω⊂RN (N ≥ 2) is a bounded smooth domain, V is an indefinite weight function which can change sign in Ω and p,q:Ω¯→(1,+∞) are continuous functions.

Keywords: p(x)-Laplacian; Robin problem; Critical point theorem (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:457-468

DOI: 10.1016/j.amc.2018.03.052

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