High order periodic impulsive problems

The theory of impulsive problem is experiencing a rapid developmentin the last few years. Mainly because they have been used to describesome phenomena, arising from different disciplines like physics or biology, subjectto instantaneous change at some time instants called moments. Secondorder periodic impulsive problems were studied to some extent, however veryfew papers were dedicated to the study of third and higher order impulsiveproblems.The high order impulsive problem considered is composed a fully nonlinearequation 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