Electron. J. Diff. Eqns., Vol. 2006(2006), No. 40, pp. 1-12.

On the $\psi$-dichotomy for homogeneous linear differential equations

Pham Ngoc Boi

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.

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Pham Ngoc Boi
Department of Mathematics
Vinh University
Vinh City, Vietnam
email: pnboi_vn@yahoo.com

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