Qualitative properties and support compactness of solutions for quasilinear Schrödinger equation with sign changing potentials

Abstract

In this paper, we deal with the following general elliptic equation involving the weigh p-Laplace operator : −Δpu+V(x)u=a(x)|u|q−1u,x∈RN,where N≥3, p≥2, 0<q, and a(x),V(x) change sign in RN. The main result of this work, establishes some qualitative properties of the solutions of the above equation. More precisely, in a first part we study the compactness of support of classical solutions. In the second part, we study the behavior and the qualitative properties of the radial classical solutions and we give a classification of these solutions.