Existence and multiplicity of solutions for nonlocal systems involving fractional Laplacian with non-differentiable terms

Abstract

In this paper, we devote to the study of the existence and multiplicity of solutions of nonlocal systems involving fractional Laplacian with non-differentiable terms using some extended critical point theorems for locally Lipschitz function on product spaces.

Keywords:

• Nonlocal systems
• fractional Laplacian
• locally Lipschitz
• index theory

AMS Subject Classifications:

• 34C25
• 58E30
• 47H04

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported by the NSFC [grant number 11501403]; and the Shanxi Province Science Foundation for Youths [grant number 2013021001-3]. The second author is supported by the NSFC [grant number 11261070].