Electron. J. Diff. Eqns., Vol. 2007(2007), No. 52, pp. 1-10.

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

Pham Ngoc Boi

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.

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

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