Higher order periodic impulsive problems,

Abstract

The theory of impulsive problem is experiencing a rapid development in the last few years. Mainly because they have been used to describe some phenomena, arising from different disciplines like physics or biology, subject to instantaneous change at some time instants called moments. Second order periodic impulsive problems were studied to some extent, however very few papers were dedicated to the study of third and higher order impulsive problems. The high order impulsive problem considered is composed a fully nonlinear equation with periodic boundary conditions, and impulsive conditions given by real valued functions satisfying some adequate conditions The arguments applied make use of the lower and upper solution method combined with an iterative technique, which is not necessarily monotone, together with classical results such as Lebesgue Dominated Convergence Theorem, Ascoli-Arzèla Theorem and fixed point theory.