Singular periodic impulse problems

Abstract

Abstract.Existence principle for the impulsive periodic boundary value problem u + c u = g(x) + e(t), u(is established, where g ∈ C(0, ∞) can have a strong singularity at the origin. Furthermore, we assume that 0 < t 1 < . .The principle is based on an averaging procedure similar to that introduced by Manásevich and Mawhin for singular periodic problems with p -Laplacian in [11]. Mathematics Subject Classification 2000. 34B37, 34B15, 34C25 Keywords. impulses, periodic solutions, topological degree PreliminariesStarting with Hu and Lakshmikantham [7], periodic boundary value problems for nonlinear second order impulsive differential equations of the formhave been studied by many authors. Usually it is assumed that the function f : [0, T ] × R 2 → R fulfils the Carathéodory conditions, 0 < t 1 < t 2 < . . . < t m < T are fixed points of the interval [0, T ] (1.4) 1