Infinitely many solutions for an anisotropic differential inclusion on unbounded domains

We consider the differential inclusion problem given by & sum;i=1 partial derivative/partial derivative xi (|partial derivative u partial derivative xi|( pi(x)-2)partial derivative u/partial derivative xi! ) +V(x)|u(x)|p(N-2)(o)u is an element of a(x)partial derivative F(x,u), in R-N. The problem deals with the anisotropicp(x)-Laplacian operator where pi are Lipschitz continuous functions 2 <= pi(x)<N for all x is an element of R(N )and i is an element of {1, . . . ,N}.Assumepo N(x) =max1 <= i <= Npi(x),a is an element of L1+(R-N)boolean AND LN po N(x)-1(R-N),F(x,t)is locally Lipschitz in the t-variable integrand and partial derivative F(x,t)is the subdifferential with respect to the t-variable in the sense of Clarke. By establishing the existence of infinitely many solutions, we achieve a first result within the anisotropic framework.