Electron. J. Diff. Eqns., Vol. 2009(2009), No. 05, pp. 1-12.

$\Psi$-bounded solutions for linear differential systems with Lebesgue $\Psi$-integrable functions on $\mathbb{R}$ as right-hand sides

Aurel Diamandescu

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 6, 2009.
Math Subject Classifications: 34D05, 34C11.
Key Words: Psi-bounded; Psi-integrable.

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Aurel Diamandescu
University of Craiova
Department of Applied Mathematics
13, ``Al. I. Cuza'' st., 200585, Craiova, Romania
email: adiamandescu@central.ucv.ro

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