Mountain pass theorem in ordered Banach spaces and its applications to semilinear elliptic equations

Abstract

In this paper, we establish a mountain pass theorem in an ordered Banach space, which is a Riesz-Banach space such that the absolute value is continuous. Applying our theorem to semilinear elliptic equations with sign-changing nonlinear terms, we prove the existence of a positive solution. © 2011 Springer Basel AG.