Study review: The existence of strong and weak solutions to Banach spaces in mathematical differential equations.

An investigation of the use of Banach spaces for finding solutions to non-linear differential equations is conducted in this paper, focusing on weak and strong solutions. We present 12 theorems and several mathematical assumptions to support the findings, which conclude that, under certain conditions, at least one weak solution for the non-linear differential Equation is obtained in Banach spaces. Furthermore, it is suggested in the paper that the same result can be obtained by expanding upon the compactness assumption. The properties of weak and strong solutions of non-linear differential equations using Banach spaces are improved upon by this research, and its potential real-world applications are highlighted. [ABSTRACT FROM AUTHOR]