Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 05, pp. 1-12.

Title:  $\Psi$-bounded solutions for linear differential
        systems with  Lebesgue $\Psi$-integrable functions on $\mathbb{R}$
        as right-hand sides
   
Author: Aurel Diamandescu (Univ. of Craiova, Romania)

Abstract:
 In this paper we give a characterization for the existence
 of $\Psi$-bounded solutions on $\mathbb{R}$ for the system
 $x'=A(t)x + f(t)$, assuming that $f$ is a Lebesgue $\Psi$-integrable
 function on $\mathbb{R}$. In addition, we give a result in connection
 with the asymptotic behavior of the $\Psi$-bounded solutions of this system. 
 
Submitted October 9, 2008. Published January 06, 2009.
Math Subject Classifications: 34D05, 34C11.
Key Words:  $\Psi$-bounded; $\Psi$-integrable.