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June  2004, 3(2): 291-300. doi: 10.3934/cpaa.2004.3.291

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, Vietnam

Received  January 2003 Revised  January 2004 Published  March 2004

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: quasi periodic solution., almost periodic solution, Neutral functional differential equation.
Mathematics Subject Classification: 34K14, 34K0.
Citation: Nguyen Minh Man, Nguyen Van Minh. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Communications on Pure & Applied Analysis, 2004, 3 (2) : 291-300. doi: 10.3934/cpaa.2004.3.291
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