Existence result for impulsive third order periodic boundary value problems

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative technique, which need not be monotone. Keywords: Third order nonlinear ordinary di¤erential equation; impulsive effects; periodic solutions; a priori estimates; lower and upper solutions; Ascoli Arzela theorem. AMS Subject Classi…cation:34B37-34B15