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

Pages: 291 - 300, Volume 3, Issue 2, June 2004

doi:10.3934/cpaa.2004.3.291       Abstract        Full Text (199.5K)       Related Articles

Nguyen Minh Man - Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam, Vietnam (email)
Nguyen Van Minh - Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam (email)

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.

Received: January 2003;      Revised: January 2004;      Published: March 2004.