Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 102, pp. 1-9.

Title: Behavior at infinity of psi-evanescent solutions to linear
       differential equations
       
Author: Pham Ngoc Boi (Vinh Univ., Vinh City, Vietnam)

Abstract:
 In this article we present some necessary and sufficient
 conditions for the existence of $\psi$-evanescent solution of the
 nonhomogeneous linear differential equation $x'=A(t)x+f(t)$, which
 is related to  the notion of  $\psi$-ordinary dichotomy for the
 equation $x'=A(t)x$. We associate that with the condition of
 $\psi$-ordinary dichotomy for the homogeneous linear differential
 equation $x'=A(t)x$.

Submitted April 29, 2010. Published July 28, 2010.
Math Subject Classifications: 34A12, 34C11, 34D05.
Key Words: psi-bounded solutions; psi-ordinary dichotomy; 
           psi-evanescent solutions