Qualitative properties and support compactness of solutions for quasilinear Schrödinger equation with sign changing potentials. (September 2020)

• Record Type: Journal Article
• Authors: Bedoui, Nizar; Ounaies, Hichem
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35J60 -- 35J91 -- 58E30; Schrödinger equation -- Indefinite potentials -- Compactly supported solution -- Radial solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111843
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we deal with the following general elliptic equation involving the weigh p-Laplace operator : − Δ p u + V ( x ) u = a ( x ) | u | q − 1 u, x ∈ R N, where N ≥ 3, p ≥ 2, 0 < q, and a ( x ), V ( x ) change sign in R N . 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.