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

Article Contents

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

This issue Previous Article Effects of small viscosity and far field boundary conditions for hyperbolic systems Next Article Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index

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: January 2003

Revised: January 2004

Published: June 2004

Abstract / Introduction Related Papers Cited by

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.

Citation:

Article Metrics

HTML views() PDF downloads(89) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content