Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 863193, 11 pages
doi:10.1155/2010/863193
Research Article

Resonance and Nonresonance Periodic Value Problems of First-Order Differential Systems

Fengqin Zhang1 and Jurang Yan1,2

1Department of Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Received 22 November 2009; Accepted 27 January 2010

Academic Editor: Guang Zhang

Copyright © 2010 Fengqin Zhang and Jurang Yan. 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

Resonance and nonresonance periodic value problems of first-order differential systems are studied. Several new existence and uniqueness of solutions for the above problems are obtained. To establish such results sufficient conditions of limit forms are given. A necessary and sufficient condition for existence of nontrivial solution is also proved.