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

This article concerns the second-order differential equation with integral boundary conditions
 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.

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

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