Infinitely many sign-changing solutions to a conformally invariant integral equation on Rn. (January 2022)

• Record Type: Journal Article
• Authors: Gluck, Mathew
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 45G15 -- 35G50; Conformally invariant -- Non linear integral equation -- Fractional Laplacian; 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.2021.112567
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work we consider the Euler–Lagrange equation for the critical points of a functional related to the conformal exponent case of the classical Hardy–Littlewood–Sobolev inequality. By lifting the problem to the sphere and leveraging the symmetries of the lifted problem, the existence of an unbounded sequence of sign-changing solutions is established. As a consequence, the existence of an unbounded sequence of sign-changing solutions to a non linear system of equations involving the fractional Laplacian is obtained.