On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations

Nguyen Minh Man; Nguyen Van Minh

doi:10.3934/cpaa.2004.3.291

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2004, Volume 3, Issue 2: 291-300. Doi: 10.3934/cpaa.2004.3.291

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On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations

Nguyen Minh Man^1, and
Nguyen Van Minh^2,

1.
Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam
2.
Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi

Received: December 31, 2002

Revised: December 31, 2003

Published: May 2004

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Abstract

This paper is concerned with the existence of almost periodic solutions of neutral functional differential equations of the form $\frac{d}{dt}Dx_t = Lx_t+f(t)$, where $D,$ $L$ are bounded linear operators from $\mathcal C$ :$ = C([-r, \quad 0],\quad \mathbb C^n )$ to $\mathbb C^n$, $f$ is an almost (quasi) periodic function. We prove that if the set of imaginary solutions of the characteristic equations is bounded and the equation has a bounded, uniformly continuous solution, then it has an almost (quasi) periodic solution with the same set of Fourier exponents as $f$.

Keywords:

Neutral functional differential equation,
almost periodic solution,
quasi periodic solution.

Mathematics Subject Classification: 34K14, 34K06.

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