Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 40, pp. 1-12.
Title: On the $\psi$-dichotomy for homogeneous
linear differential equations
Author: Pham Ngoc Boi (Vinh Univ., Vietnam)
Abstract:
In this article we present some conditions for the
$\psi$-dichotomy of the homogeneous linear differential equation
$x'=A(t)x$. Under our condition every $\psi$-integrally bounded
function $f$ the nonhomogeneous linear differential equation
$x'=A(t)x +f(t)$ has at least one $\psi$-bounded solution on
$(0,+\infty)$.
Submitted December 18, 2005. Published March 26, 2006.
Math Subject Classifications: 34A12, 34C11, 34D05.
Key Words: $\psi$-bounded; $\psi$-integrable;
$\psi$-integrally bounded; $\psi$-exponential.