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

Cabada, Alberto

doi:https://doi.org/10.1155/S1048953394000043

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∈ℝ,i=0,…,n−1 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 n≥3 with either α≤β or α≥β.For this, we study some maximum principles for the operator Lu≡u(n)+Mu. Furthermore, we obtain a generalization of the method of mixed monotonicity considering f and u as vectorial functions.

Copyright

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.

International Journal of Stochastic Analysis

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

Abstract

Copyright