Psi-exponential dichotomy for linear differential equations in a Banach space

Abstract

In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banach space. With these two concepts we prove the existence of psi-bounded solutions of the appropriate inhomogeneous equation. A roughness of the psi-dichotomy is also considered.

Keywords

• Dichotomy for ordinary differential equations
• psi-dichotomy
• psi-boundedness
• psi-stability