On the correct formulation of a nonlinear differential equations in Banach space - Mahmoud M. El-Borai; Osama L. Moustafa; Fayez H. Michael (International Journal of Mathematics and Mathematical Sciences)
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.