Positive solutions for a Kirchhoff-type problem involving multiple competitive potentials and critical Sobolev exponent. (September 2020)

• Record Type: Journal Article
• Authors: Fan, Haining
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35A15 -- 35B33 -- 35J62; Multiple positive solutions -- Kirchhoff-type problem -- Critical Sobolev exponent -- Competitive potentials; 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.2020.111869
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the existence and multiplicity of positive solutions for a Kirchhoff-type problem involving several potentials and critical nonlinearities on unbounded domain. The first main result is that the problem possesses a ground state solution concentrating around a concrete set relates to the potentials. The second one is that with the help of Nehari manifold and Ljusternik–Schnirelmann category, the relationship between the number of positive solutions and the category of the global minima set of a suitable ground energy function is established. Moreover, we present a sufficient condition for the nonexistence of ground state solution.