Existence of solution for a degenerate p(x)p(x)-Laplacian equation in RNRN

Using variational methods we establish the existence of nontrivial solutions for the following class of problems−div(a(x)|∇u|p(x)−2∇u)+|u|p(x)−2u=K(x)|u|q(x)−2uinRN, where p,q,a,K:RN→R are continuous functions satisfying some conditions and the set {x∈RN;a(x)=0} is not empty.