Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 157-165
A generalized upper and lower solutions method for nonlinear second order ordinary differential equations
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
Copyright © 1992 Juan J. Nieto and Alberto Cabada. 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.
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.