Infinitely many solutions for Kirchhoff problems with lack of compactness. (August 2020)

• Record Type: Journal Article
• Authors: Zhang, Youpei; Tang, Xianhua; Qin, Dongdong
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 35J60 -- 35J20; Infinitely many solutions -- Morse index -- Kirchhoff problem -- Local Pohožaev identity; 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.2020.111856
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the following Kirchhoff problem: − ( 1 + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( u ), x ∈ R 3, u ∈ H 1 ( R 3 ), where b is a positive constant. Assume that f ( u ) is an odd function of u . Under some appropriate assumptions on V but without radial symmetry or compactness hypotheses, we establish the existence of infinitely many solutions to the above problem by using an approximation method employed by Sato and Shibata (2018) and some new arguments.