Electron. J. Diff. Eqns., Vol. 2008(2008), No. 25, pp. 1-6.

Existence of solutions for some third-order boundary-value problems

Zhanbing Bai

In this paper concerns the third-order boundary-value problem
 u'''(t)+ f(t, u(t),u'(t), u''(t))=0, \quad 0 < t < 1, \cr
 r_1 u(0) - r_2 u' (0)= r_3 u(1) + r_4 u'(1)= u''(0)=0.
By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The construction of lower or upper solutions is also presented.

Submitted September 21, 2007. Published February 22, 2008.
Math Subject Classifications: 34B15.
Key Words: Third-order boundary-value problem; lower and upper solutions; fixed-point theorem.

Show me the PDF file (189 KB), TEX file, and other files for this article.

Zhanbing Bai
Institute of Mathematics
Shandong University of Science and Technology
Qingdao 266510, China
email: zhanbingbai@163.com

Return to the EJDE web page