In this article, we study the following problem with Navier boundary conditions (jujp(x)2u) + jujp(x)2u = jujq(x)2u + juj (x)2u in ; u = u = 0 on @ : where is a bounded domain in RN with smooth boundary @ , N 1. p(x); q(x) and (x) are continuous functions on , and are parameters. Using variational methods, we establish some existence and non-existence results of solutions for this problem.
