Two homoclinic solutions of anonperiodic fourth-order impulsive differential equation

Abstract

In this paper, we are concerned with a kind of nonperiodic fourth-order impulsive differential equation. By applying the mountain pass theorem, we shall establish several new criteria for the existence of at least two nontrivial homoclinic solutions of the addressed equation. Some recent results in the literature are generalized and improved. In addition, a numerical example is provided to show the applicability and effectiveness of our main results.

Mathematics Subject Classification (2010): 34C37, 37J45.

Keywords: Homoclinic solutions, fourth-order impulsive differential equation, nonperiodic, mountain pass theorem