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

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.