Journal of Applied Mathematics and Stochastic Analysis 
Volume 9 (1996), Issue 1, Pages 11-20
doi:10.1155/S1048953396000020

Periodic solutions of quasi-differential equations

Abdelkader Boucherif,1 Eduardo García-Río,2 and Juan J. Nieto2

 1University of Tlemcen, Department of Mathematics, BP 119, Tlemcen 13000, Algeria
2Universidad de Santiago de Compostela, Departamento de Análisis Matematico, Facultad de Matemáticas, Spain
Received 1 January 1995; Revised 1 December 1995

Abstract

Existence principles and theorems are established for the nonlinear problem Lu=f(t,u) where Lu=−(pu′)′+hu is a quasi-differential operator and f is a Carathéodory function. We prove a maximum principle for the operator L and then we show the validity of the upper and lower solution method as well as the monotone iterative technique.