Further study on periodic solutions of elliptic equations with a fractional Laplacian

2017/10/13 by Zhuoran Du, Changfeng Gui, Du, Zhuoran +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1710.05043

openalex publication_date 2017/10/13 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

We obtain some existence theorems for periodic solutions to several linear 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.

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