Further study on periodic solutions of elliptic equations with a fractional Laplacian. (April 2020)

• Record Type: Journal Article
• Authors: Du, Zhuoran; Gui, Changfeng
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: 35J61 -- 35B10 -- 35A01 -- 58J55; Periodic solutions -- Fractional Laplacian -- Bifurcation -- Hamiltonian identity -- Modica-type inequalities; 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.2019.01.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain some existence theorems for periodic solutions to several linear and nonlinear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not larger than some exact positive constant. Hamiltonian identity, Modica-type inequalities and an estimate of the energy for periodic solutions are also established.