International Journal of Mathematics and Mathematical Sciences 
Volume 26 (2001), Issue 7, Pages 437-444
doi:10.1155/S0161171201002307

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

Mahmoud M. El-Borai, Osama L. Moustafa, and Fayez H. Michael

 Faculty of Science, Alexandria University, Alexandria, Egypt
Received 28 September 1998

Abstract

We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1)(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.