Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 567319, 10 pages
http://dx.doi.org/10.1155/2011/567319
Research Article

Positive Almost Periodic Solution on a Nonlinear Differential Equation

Ni Hua, Tian Li-xin, and Liu Xun

Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 17 March 2011; Accepted 10 July 2011

Academic Editor: Jitao Sun

Copyright © 2011 Ni Hua et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the following nonlinear equation 𝑑 𝑥 ( 𝑡 ) / 𝑑 𝑡 = 𝑥 ( 𝑡 ) [ 𝑎 ( 𝑡 ) − 𝑏 ( 𝑡 ) 𝑥 𝛼 ( 𝑡 ) − 𝑓 ( 𝑡 , 𝑥 ( 𝑡 ) ) ] + 𝑔 ( 𝑡 ) , by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.