Eigenvalues of the p(x)-Laplacian Steklov problem☆

By Shao-Gao Deng. 2008

94 citations recorded by the source corpus.

Abstract Consider Steklov eigenvalue problem involving the p ( x ) -Laplacian on a bounded domain Ω , the open subset of R N with N ⩾ 2 , as follows { Δ p ( x ) u = | u | p ( x ) − 2 u in Ω , | ∇ u | p ( x ) − 2 ∂ u ∂ γ = λ | u | p ( x ) − 2 u on ∂ Ω , where p ( x ) ≢ constant. We prove that the existence of infinitely many eigenvalue sequences. Unlike the p -Laplacian case, for a variable exponent p ( x ) (≢ constant), there does not exist a principal eigenvalue and the set of all eigenvalues is not closed under some assumptions. Finally, we present some sufficient conditions for the infimum of all eigenvalues is zero and positive, respectively.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cb251d1cdc4bafd9efa110d126fa9ead3b7c4265

Citations in the corpus

• Overview of differential equations with non-standard growth (2010, unknown): “Deng [69] considered the eigenvalue problem with λ = −1, and non-homogeneous Neumann boundary conditions |∇u|p(x)−2 ∂u ∂γ = μ |u| p(x)−2u, x ∈ ∂Ω, (5.”