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

Abstract

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 $\mathbb{R}_+$.

Keywords

• $\psi$-dichotomy for ordinary differential equations
• $\psi$-boundedness.