Monotone iterations for differential equations with a parameter

Jankowski, Tadeusz; Lakshmikantham, V.

doi:https://doi.org/10.1155/S1048953397000348

International Journal of Stochastic Analysis

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Volume 10 |Article ID 671410 | https://doi.org/10.1155/S1048953397000348

Tadeusz Jankowski, V. Lakshmikantham, "Monotone iterations for differential equations with a parameter", International Journal of Stochastic Analysis, vol. 10, Article ID 671410, 6 pages, 1997. https://doi.org/10.1155/S1048953397000348

Monotone iterations for differential equations with a parameter

Tadeusz Jankowski¹ and V. Lakshmikantham²

¹Technical University of Gdansk, Department of Numerical Analysis, Poland

²Florida Institute of Technology, Applied Mathematics Program, USA

Received01 Feb 1997

Revised01 Jun 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.

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Copyright © 1997 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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