On $Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $R$

M. S. N. Murty, Acharya Nagarjuna University - Nuzvid Campus, Nuzvid, India.
G. Suresh Kumar, Koneru Lakshmaiah University, Vaddeswaram, India.

E. J. Qualitative Theory of Diff. Equ., No. 62. (2009), pp. 1-12.

Abstract: In this paper we provide necesssary and sufficient conditions for the existence of at least one $\Psi$-bounded solution on $\mathbb{R}$ for the system $X'=A(t)X +XB(t)+F(t)$, where $F(t)$ is a Lebesgue $\Psi$-integrable matrix valued function on $\mathbb{R}$. Further, we prove a result relating to the asymptotic behavior of the $\Psi$-bounded solutions of this system.

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