The Existence of Periodic Solutions for Second Order Functional Differential Equations Caused by Impulses Effects

Abstract

The existence for solutions of the periodic boundary value problems concerning the second order impulsive functional differential equation (Equations) and the boundary conditions x(0) = x(T), x'(0) = x'(T) at resonance case are established. The method is based upon the theory of coincidence due to Mawhin, which shows that the impulse infects cause the existence of solutions. Related examples are mentioned to support the results of this paper.

Key words and phrases. Periodic boundary value problem, coincidence degree theory of Mawhin, second order impulsive functional differential equation.

2000 Mathematics Subject Classification. 34B15, 34B10