Eigenvalues for a Neumann Boundary Problem Involving the p(x)‐Laplacian

Qing Miao

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: We study the existence of weak solutions to the following Neumann problem involving the p(x)‐Laplacian operator: −Δp(x)u + e(x) | u|p(x)−2u = λa(x)f(u), in Ω, ∂u/∂ν = 0, on ∂Ω. Under some appropriate conditions on the functions p, e, a, and f, we prove that there exists λ¯>0 such that any λ∈(0,λ¯) is an eigenvalue of the above problem. Our analysis mainly relies on variational arguments based on Ekeland’s variational principle.

Date: 2015
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https://doi.org/10.1155/2015/632745

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:632745

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