Existence of solutions of nonlinear differential equations with $psi$-exponential or $psi$-ordinary dichotomous linear part in a Banach space

摘要

In this article we consider nonlinear differential equations with $psi$-exponential and $psi$-ordinary dichotomous linear part in a Banach space. By the help of the fixed point principle of Banach sufficient conditions are found for the existence of $psi$-bounded solutions of these equations on $mathbb{R}$ and $mathbb{R}_+$.