Electron. J. Diff. Equ., Vol. 2012 (2012), No. 45, pp. 1-9.

Solvability of second-order boundary-value problems at resonance involving integral conditions

Yujun Cui

Abstract:
This article concerns the second-order differential equation with integral boundary conditions
$$\displaylines{ x''(t)=f(t,x(t),x'(t)),\quad t\in (0,1),\cr x(0)=\int_0^1x(s)d\alpha(s),\quad x(1)=\int_0^1x(s)d\beta(s). }$$
Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.

Submitted December 26, 2011. Published March 20, 2012.
Math Subject Classifications: 34B15.
Key Words: Coincidence degree; integral boundary-value problem; resonance.

An addendum was attached on March 30, 2012. It corrects several mistakes and provides additional references. See page 10 of this article.

Show me the PDF file (207 KB), TEX file, and other files for this article.

Yujun Cui
Institute of Mathematics
Shandong University of Science and Technology
Qingdao 266590, China
email: cyj720201@163.com

Return to the EJDE web page