International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1994 / Article

Open Access

Volume 7 |Article ID 737583 | 15 pages | https://doi.org/10.1155/S1048953394000043

The method of lower and upper solutions for n th-order periodic boundary value problems

Received01 Aug 1993
Revised01 Jan 1994

Abstract

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(n)(t)=f(t,u(t));u(i)(a)u(i)(b)=λi,i=0,,n1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n3 with either αβ or αβ.For this, we study some maximum principles for the operator Luu(n)+Mu. Furthermore, we obtain a generalization of the method of mixed monotonicity considering f and u as vectorial functions.

Copyright © 1994 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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