Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 3, Pages 273-278
doi:10.1155/S1048953397000348

Monotone iterations for differential equations with a parameter

Tadeusz Jankowski1 and V. Lakshmikantham2

1Technical University of Gdansk, Department of Numerical Analysis, Gdansk, Poland
2Florida Institute of Technology, Applied Mathematics Program, Melbourne 32901, FL, USA

Received 1 February 1997; Revised 1 June 1997

Copyright © 1997 Tadeusz Jankowski and V. Lakshmikantham. 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.

Abstract

Consider the problem {y′(t)=f(t,y(t),λ),t∈J=[0,b],y(0)=k0,G(y,λ)=0.. Employing the method of upper and lower solutions and the monotone iterative technique, existence of extremal solutions for the above equation are proved.