Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 13, pp. 1-11.
Title: Solvability for second-order m-point boundary value problems
at resonance on the half-line
Authors: Yang Liu (Hefei Teachers College, China)
Dong Li (Jiamusi Univ., China)
Ming Fang (Yanbian Univ., Yanji, China)
Abstract:
In this article, we investigate the existence of positive
solutions for second-order m-point boundary-value problems
at resonance on the half-line
$$\displaylines{
(q(t)x'(t))'=f(t,x(t),x'(t)),\quad \hbox{a.e. in }(0,\infty), \cr
x(0)=\sum_{i=1}^{m-2}\alpha_ix(\xi_i),\quad
\lim_{t\to \infty}q(t)x'(t)=0.
}$$
Some existence results are obtained by using the Mawhin's
coincidence theory.
Submitted July 8, 2008. Published January 12, 2009.
Math Subject Classifications: 34B15.
Key Words: m-point boundary value problem; resonance; half-line;
coincidence degree theory.