Applications of Morse Theory to Fourth-Order Impulsive Differential Equations ∗

Abstract

This paper is devoted to studying the nontrivial solutions for fourth-order impulsive differential equations. By applying Morse theory and combining it with local linking theory, some new criteria to guarantee that the fourth-order impulsive differential equation has at least one nontrivial solution will be given. Then, we give an example to illustrate the effectiveness and feasibility of the obtained results in our paper. Moreover, some previous corresponding results will be significantly improved in our paper.