Existence of infinitely many solutions for a Neumann problem involving the p(x)-Laplacian☆

By Xianling Fan, Chao Ji. 2007

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Abstract In this paper we consider the Neumann problem involving the p ( x ) -Laplacian of the type { − div ( | ∇ u | p ( x ) − 2 ∇ u ) + λ ( x ) | u | p ( x ) − 2 u = f ( x , u ) + g ( x , u ) in Ω , ∂ u ∂ γ = 0 on ∂ Ω . We prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces. Our results are an improvement and generalization of the relative results obtained by B. Ricceri for the p -Laplacian case.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fb2d7cb2f1d18a0a4f61a7224b7658c068a866d1