Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 153, pp. 1-13.

Title: Psi-exponential dichotomy for linear differential equations in a Banach space
        
Authors: Atanaska Georgieva (Univ. of Plovdiv, Bulgaria)
         Hristo Kiskinov    (Univ. of Plovdiv, Bulgaria)
         Stepan Kostadinov  (Univ. of Plovdiv, Bulgaria)
         Andrey Zahariev    (Univ. of Plovdiv, Bulgaria)

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.

Submitted March 28, 2013. Published July 02, 2013.
Math Subject Classifications: 34G10, 34D09, 34C11.
Key Words: Dichotomy for ordinary differential equations;
           psi-dichotomy; psi-boundedness; psi-stability.