We consider a class of first-order impulsive functional differential equations, where the functional dependence is not necessarily a Lipschitzian function. The new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented. We give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution. © 2005 Elsevier Inc. All rights reserved.
Nieto, J. J., & Rodríguez-López, R. (2006). Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations. Journal of Mathematical Analysis and Applications, 318(2), 593–610. https://doi.org/10.1016/j.jmaa.2005.06.014