Periodic solutions in fading memory spaces

Khalil Ezzinbi; James H. Liu; Nguyen Van Minh

doi:10.3934/proc.2005.2005.250

Article Contents

2005, Volume 2005: 250-257. Doi: 10.3934/proc.2005.2005.250 open access

This issue Previous Article Numerical results for floating drops Next Article Dynamics of the discrete Chaplygin sleigh

Periodic solutions in fading memory spaces

1.
Department de Mathematiques, Faculte des Sciences Semlalia, B.P. 2390, Marrakech, Morocco
2.
Department of Mathematics, James Madison University, Harrisonburg, VA 22807
3.
Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807

Received: August 31, 2004

Revised: February 28, 2005

Published: August 2005

Abstract Related Papers Cited by

Abstract

For $A(t)$ and $f(t,x,y)$ $T$-periodic in $t$, consider the following evolution equation with infinite delay in a general Banach space $X$, $$u^\prime (t)+ A(t)u(t)=f(t,u(t),u_t),\;\; t> 0,\;\;u(s) =\phi (s),\;\;s \leq 0, $$ where the resolvent of the unbounded operator $A(t)$ is compact, and $u_t (s)=u(t+s),\; s\leq 0$. We will work with general fading memory phase spaces satisfying certain axioms, and derive periodic solutions. We will show that the related Poincar\'{e} operator is condensing, and then derive periodic solutions using the boundedness of the solutions and some fixed point theorems. This way, the study of periodic solutions for equations with infinite delay in general Banach spaces can be carried to fading memory phase spaces. In doing so, we will improve a condition of [4] and extend the results of [7,8].

Keywords:

Mathematics Subject Classification: 34G.

Citation:

Article Metrics

HTML views() PDF downloads(88) Cited by(0)

Periodic solutions in fading memory spaces

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Periodic solutions in fading memory spaces

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content