On third order generalized periodic impulsive problems

Abstract

This work concerns to third order impulsive problems with the fully nonlinear equation u'''(x) = f (x; u (x) ; u' (x) ; u'' (x)) in [0, 1] without the impulsive points, with f defined in [0, 1]xR4, real valued, a L1-Carathéodory function, the periodic boundary conditions u^(i) (0) = u^(i) (1) ; i = 0; 1; 2; and the impulsive effects given by generalized continuous functions, nondecreasing in all variables.