Beyond the Mountain Pass: Some Applications
Ireneo Peral · Advanced Nonlinear Studies · 2012
Abstract We will survey three applications of the famous Mountain Pass Lemma by Antonio Ambrosetti and Paul H. Rabinowitz, [6]. Precisely, we will present some results on the following problems: A model of growth and roughening of surfaces, usually called Kardar-Parisi-Zhang model. A supercritical problem involving Hardy-Leray potential with the pole at the boundary. A fourth order nonlinear problem related to epitaxial growth. The common characteristic of all these problems is that we have some extra difficulties in order to apply the Mountain Pass Lemma.