International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1996 / Article

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Volume 9 |Article ID 241932 | 10 pages | https://doi.org/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

Received01 Jan 1995
Revised01 Dec 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.

Copyright © 1996 Hindawi Publishing Corporation. 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.

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