Nonlinear Elliptic Equations in Strip-Like Domains

Abstract

We study the existence of a positive solution of a nonlinear elliptic equation [GRAPHICS] where k >= 2 and D is a bounded domain in R-l, l >= 1. We give almost necessary and sufficient condition on f(xi) for the existence of a positive solution, which is inspired by the works of Berestycki-Lions [1] and Berestycki-Gallouet-Kavian [3].