Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 45, pp. 1-9.
Title: Solvability of second-order boundary-value problems at resonance
involving integral conditions
Authors: Yujun Cui (Shandong Univ. of Science and Tech., Qingdao, China)
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.
An addendum was attached on March 30, 2012. It corrects several mistakes and provide additional references. See page 10 of this article.
Submitted December 26, 2011. Published March 20, 2012.
Math Subject Classifications: 34B15.
Key Words: Coincidence degree; integral boundary-value problem; resonance.