Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 52, pp. 1-10.

Title: Existence of $\psi$-bounded solutions for nonhomogeneous linear
       differential equations

Author: Pham Ngoc Boi (Vinh Univ., Vinh City, Vietnam)

Abstract:
 In this article we present a necessary and sufficient condition
 for the existence of $\psi$-bounded solution on $\mathbb{R}$ of
 the nonhomogeneous linear differential equation $x'=A(t)x+f(t)$.
 We associate that with the condition of the concept $\psi$-dichotomy
 on $\mathbb{R}$ of the homogeneous linear differential equation
 $x'=A(t)x$.
  
Submitted January 26, 2007. Published April 5, 2007.
Math Subject Classifications: 34A12, 34C11, 34D05.
Key Words: $\psi$-bounded solution; $\psi$-integrable;
           $\psi$-integrally bounded; 
           $\psi$-exponential dichotomy.