Solutions to Perturbed Eigenvalue Problems of the p-Laplacian in R(N)

Abstract

Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem Δpu=f(x,u) in R(N). Under the assumptions that the primitive F(x,u) of f(x,u) interacts only with the first eigenvalue, we look for solutions in the space D{1,p}({ RN). Furthermore, we assume a condition that measures how different the behavior of the function F(x,u) is from that of the p-power of u.