Existence of saddle solutions of a nonlinear elliptic equation involving p-Laplacian in more even-dimensional spaces

Abstract

We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p > 2, -Δpu = f(u) in R2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m ≥ 2p.