Positive solutions to Schrödinger-Kirchhoff equations with inverse potential. Issue 4 (3rd April 2022)

• Record Type: Journal Article
• Authors: Luo, Linfeng; Guo, Zuji
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 4(2022)
• Page Start: 1012
• Page End: 1029
• Publication Date: 2022-04-03
• Subjects: T. Bartsch; Bound state solutions -- ground state solutions -- Schrödinger-Kirchhoff-type equations -- linking theorem -- pohozaev identity; 35J20 -- 35J65; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1843642
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : This paper is concerned with the existence of positive solutions to Schrödinger-Kirchhoff-type equations 1 ( P ) − a + b ∫ R 3 | ∇ u | 2 Δ u + V ( x ) u = | u | p − 1 u i n R 3, u ∈ H 1 ( R 3 ), where a and b are two positive constants, p ∈ ( 1, 5 ) and V : R 3 → R is a potential function. Under certain assumptions on V, we prove that ( P ) has no ground state solution. However, we can show ( P ) has a positive bound state solution by applying a new version of the global compactness lemma and the linking theorem.