Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

Abstract

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.

Keywords:

• Multiple solutions
• sign-changing solution
• invariant sets of descending flow
• second-order functional difference equation

2000 Mathematics Subject Classifications:

• Primary: 39A14
• Secondary: 34C37

Acknowledgements

The author gratefully acknowledges the two anonymous reviewers for their careful reading and valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the Program for Changjiang Scholars and Innovative Research Team in University [grant number IRT_16R16].