Abstract:
The study is take functions spaces and discussed functions continuous and their derivatives.
Identified the defined equations by mappings which enjoy special kinds of properties, when an introduced some special mappings.
The study is take concept the generalized derivative and how to find it, and discussed functions extension which considering basis topic in nonlinear analysis, and provided many theorems in this regarding, as well as some examples about operators such as differential operator and integral operator.
The study is take one of the main theorems in nonlinear analysis is said to be degree theorem (Mapping degree) which helped in prove global solution theorems as well as topological theorems.
Finally the study is take existence and uniqueness theorems as introduce to differential equations.
