We deal with the nonlinear impulsive periodic boundary value problem , , , , , . We establish the existence results which rely on the presence of a well-ordered pair of lower/upper functions associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functions , is not required here.
"Nonmonotone impulse effects in second-order periodic boundary value problems." Abstr. Appl. Anal. 2004 (7) 577 - 590, 29 June 2004. https://doi.org/10.1155/S1085337504306299