Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory

Abstract

In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory. Several examples are provided to illustrate applications of our results.

Keywords

• discrete kirchhoff-type problem
• nontrivial solution
• variational method
• morse theory
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