Nontrivial solutions for a nonlinear Schrödinger equation with nonsymmetric coefficients. (June 2020)

• Record Type: Journal Article
• Authors: Wang, Xiaoping; Liao, Fangfang
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J20 -- 35J65; Schrödinger equation -- Pohozaev identity -- Concentration compactness -- Cerami sequence -- Barycenter; 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.2020.111755
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is dedicated to studying the nonlinear Schrödinger equations of the form − △ u + λ u = a ( x ) f ( u ), x ∈ R N ; u ∈ H 1 ( R N ), where a ∈ C 1 ( R N, [ 0, ∞ ) ) is nonsymmetric and satisfies a ( x ) ≤ ( ⁄ ≡ ) a ∞ ≔ lim | y | → ∞ a ( y ), and f ∈ C ( R, R ) . By using concentration compactness arguments and projections on a general Pohozaev type manifold, we prove that the above problem has a nontrivial solution under weaker assumptions on a and f than the existing results in literature.