Periodic solutions of a fractional Schrödinger equation

Abstract

We consider periodic solutions of the following nonlinear equation associated with the fractional Laplacian $(-\mathrm{\Delta }{)}^{s}u(x)+V(x)u(x)=f(x,u),x\in \mathbb{R},$where $V(x)\in C(\mathbb{R})$ is T-periodic and 0 belongs to a spectral gap of the operator $(-\mathrm{\Delta }{)}^s+V$. We obtain the existence of a periodic solution by using a generalized linking theorem.

COMMUNICATED BY:

• G. A. Chechkin

Keywords:

• Fractional Schrödinger equations
• periodic solutions
• spectrum
• cerami sequence

Mathematics Subject Classification(2020):

• 35B10
• 35A01
• 35J61

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are supported by the Natural Science Foundation of Hunan Province, China [grant number 2022JJ30118].