Journal of Applied Mathematics and Stochastic Analysis 
Volume 5 (1992), Issue 2, Pages 157-165
doi:10.1155/S1048953392000133

A generalized upper and lower solutions method for nonlinear second order ordinary differential equations

Juan J. Nieto1 and Alberto Cabada2

 1Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain
2Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain
Received 1 May 1991; Revised 1 July 1991

Abstract

The purpose of this paper is to study a nonlinear boundary value problem of second order when the nonlinearity is a Carathéodory function. It is shown that a generalized upper and lower solutions method is valid, and the monotone iterative technique for finding the minimal and maximal solutions is developed.