Existence of a Least Energy Nodal Solution for a Class of Quasilinear Elliptic Equations with Exponential Growth

Abstract

In this paper we prove the existence of a least energy nodal (i.e. sign-changing) solution for a large class of quasilinear problem in a smooth bounded domain of Euclidean space. Moreover, we show that solution has exactly two nodal domains i.e. it changes sign exactly once in this domain. The proof is based on a minimization argument and a quantitative deformation lemma.