Infinitely many solutions for a differential inclusion problem in image involving the image-Laplacian Original Research Article

In this paper we consider the differential inclusion problem in RNRN involving the p(x)p(x)-Laplacian of the type View the MathML source{−div(|∇u|p(x)−2∇u)+|u|p(x)−2u∈∂F(x,u) inRN,u∈W1,p(x)(RN). Turn MathJax on We prove the existence of infinitely many radially symmetric solutions of the problem under suitable hypotheses by applying a nonsmooth variational principle due to Marano and Motreanu and the theory of the variable exponent Sobolev spaces.