Sign-changing solutions for a fractional Kirchhoff equation. (January 2020)

• Record Type: Journal Article
• Authors: Isernia, Teresa
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35A15 -- 35J60 -- 35R11 -- 45G05; Fractional Laplacian -- Potential vanishing at infinity -- Nehari manifold -- Sign-changing solutions; 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.2019.111623
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Using a minimization argument and a quantitative deformation lemma, we establish the existence of least energy sign-changing solutions for the following nonlinear Kirchhoff problem ( a + b [ u ] 2 ) ( − Δ ) s u + V ( x ) u = K ( x ) f ( u ) in R 3, where a, b > 0 are constants, s ∈ ( 0, 1 ), ( − Δ ) s is the fractional Laplacian, V, K are continuous, positive functions, allowed for vanishing behavior at infinity, and f is a continuous function satisfying suitable growth assumptions. Moreover, when the nonlinearity f is odd, we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals.