Existence of periodic solutions of second-order nonlinear random impulsive differential equations via topological degree theory

In this paper, we investigate the existence of periodic solutions for a class of second order nonlinear random impulse differential equations. By extending the definitions of continuous function bound set, curvature bound set and Nagumo set in topological degree to PC space, and defining the appropriate operators and conditions, using the theory of topological degree and coincidence degree, we prove that the solution must be bounded if it exists and find the boundary value. Finally, we define appropriate Nagumo set and autonomous curvature bound set, and obtain the existence of periodic solutions of equations and simultaneous equations by using Mawhin’s continuity theorem.