Fourth Order Impulsive Periodic Boundary Value Problems

In this work it is presented an existence result for the impulsive problem composed by the fourth order fully nonlinear equation u i v x = f x , u x , u ′ x , u ″ x , u ″ ′ x for a.e. x ∈ 0 , 1 \ x 1 , … , x m where f : 0 , 1 × R 4 → R is a L 1 -Carathéodory function, along with the periodic boundary conditions u i 0 = u i 1 , i = 0 , 1 , 2 , 3 , and the impulses u x j + = g j u x j , u ′ x j + = h j u ′ x j , u ″ x j + = k j u ″ x j , u ″ ′ x j + = l j u ″ ′ x j , where x j ∈ 0 , 1 , for j = 1 , … , m , such that 0 = x 0 < x 1 < ⋯ < x m < x m + 1 = 1 , and g j , h j , k j , l j are given real valued functions satisfying some adequate conditions. The arguments used apply lower and upper solutions technique combined with an iterative and non monotone technique.