|MSC:||34G10||Linear equations [See also 47D06, 47D09]|
|34G20||Nonlinear equations [See also 47Hxx, 47Jxx]|
A generalization of the well known dichotomies for a class of homogeneous differential
equations in an arbitrary Banach space is introduced.
The aim of this paper is the consideration of the nonlinear differential
equation with generalized dichotomous linear part. By the help of the fixpoint principle
of Banach and Schauder-Tychonoff are found sufficient conditions
for the existence of solutions of the nonlinear equation.