Electron. J. Diff. Eqns., Vol. 2006(2006), No. 25, pp. 1-8.

On second order periodic boundary-value problems with upper and lower solutions in the reversed order

Haiyin Gao, Shiyou Weng, Daqing Jiang, Xuezhang Hou

Abstract:
In this paper, we study the differential equation with the periodic boundary value
$$\displaylines{
 u''(t)=f(t, u(t), u'(t)),\quad t\in [0,  2\pi]\cr
 u(0)=u(2\pi), \quad u'(0)=u'(2\pi).
 }$$
The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.

Submitted November 7, 2005. Published February 28, 2006.
Math Subject Classifications: 34B15, 34B16.
Key Words: Periodic boundary value; existence; upper and lower solutions.

Show me the PDF file (208K), TEX file, and other files for this article.

Haiyin Gao
School of Mathematics and Statistics
Northeast Normal University
Changchun 130024, China
email: gaohaiyinhealthy@yahoo.com.cn
Shiyou Weng
Applied Science College
Changchun University
Jilin 130022, China
email: wengshiyou2001@yahoo.com.cn
Daqing Jiang
School of Mathematics and Statistics
Northeast Normal University
Changchun 130024, China
email: daqingjiang@vip.163.com
Xuezhang Hou
Mathematics Department, Towson University
Baltimore, MD 21252, USA
email: xhou@towson.edu

Return to the EJDE web page