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International Journal of Mathematics and Mathematical Sciences
Volume 26, Issue 7, Pages 437-444
http://dx.doi.org/10.1155/S0161171201002307

On the correct formulation of a nonlinear differential equations in Banach space

Faculty of Science, Alexandria University, Alexandria, Egypt

Received 28 September 1998

Copyright © 2001 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.

Abstract

We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn1/dtn1)(du/dt+Au)=B(t)u+f(t,W(t)), and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.