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

Copyright © 1996 Abdelkader Boucherif et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.