Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 40, pp. 1-12.

Title: On the $\psi$-dichotomy for homogeneous
       linear differential equations
       
Author: Pham Ngoc Boi (Vinh Univ., Vietnam)

Abstract: 
 In this article we present some conditions for the
 $\psi$-dichotomy of the homogeneous linear differential equation
 $x'=A(t)x$. Under our condition every $\psi$-integrally bounded
 function $f$ the nonhomogeneous linear differential equation
 $x'=A(t)x +f(t)$ has at least one $\psi$-bounded solution on
 $(0,+\infty)$.
  
Submitted December 18, 2005. Published March 26, 2006.
Math Subject Classifications: 34A12, 34C11, 34D05.
Key Words: $\psi$-bounded; $\psi$-integrable;
           $\psi$-integrally bounded; $\psi$-exponential.