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Publication Cover
Applicable Analysis
An International Journal
Volume 40, 1991 - Issue 1
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Original Articles

Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space

Ludwik Byszewski Department of Applied Mathematics, Florida Institute of Technology, 150 West University Boulevard, Melbourne, Florida, 32901, USA
&
V. Lakshmikantham Department of Applied Mathematics, Florida Institute of Technology, 150 West University Boulevard, Melbourne, Florida, 32901, USA
Pages 11-19 | Received 01 Jun 1990, Published online: 10 May 2007
 
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Abstract

The aim of the paper is to give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a Banach space. The Banach theorem about the fixed point is used to prove the existence and uniqueness of a solution of the problem considered. The result obtained in this paper can be applied among other things to the description of motion phenomena with better effect than the classical Cauchy problem.

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