Nonlinear Perturbations of a Periodic Quasilinear Elliptic Problem with Discontinuous Nonlinearity in RN1

Using variational methods, we estabilish existence of positive solutions for a class of quasilinearelliptic problems−∆pu+V(x)up−1=H(u−β)f(u),inRNwhere∆pu=div(|∇u|p−2∇u),β >0,2≤p < N,Vis a positive, continuous perturbations of aperiodic function,His the Heaviside function andfis a continuous function with subcritical growth.The results of the semilinear equations are extended to the quasilinear problem.