A parameterized quasilinear Schrödinger equation with indefinite potentials. (March 2020)

• Record Type: Journal Article
• Authors: Giacomoni, Jacques; Santos, Carlos Alberto; Yang, Minbo; Zhou, Jiazheng
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35J20 -- 35J60 -- 35Q55; Quasilinear Schrödinger equation -- Indefinite potential -- Critical groups -- Local linking; 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.2019.111703
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the existence of solutions for the quasilinear Schrödinger equation − Δ u − k Δ [ ( 1 + u 2 ) 1 ∕ 2 ] u 2 ( 1 + u 2 ) 1 ∕ 2 + V ( x ) u = g ( u ) in H 1 ( R N ) ∩ L l o c ∞ ( R N ), where N ≥ 3, V is a continuous potential allowed to be indefinite, g is a subcritical growth function, and k is a real parameter. By using local linking arguments and computing the critical groups of the energy functional, we obtain the existence of nontrivial solution for the equation.