Electron. J. Diff. Eqns., Vol. 2009(2009), No. 13, pp. 1-11.

Solvability for second-order m-point boundary value problems at resonance on the half-line

Yang Liu, Dong Li, Ming Fang

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.

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Yang Liu
Department of Mathematics
Hefei Teachers College
Hefei, Anhui 230061, China
email: liuyang19830206@yahoo.com.cn
Dong Li
Department of Mathematics
Jiamusi University
Jiamusi, Heilongjiang 154007, China
email: ld09281117@sohu.com
Ming Fang
Department of Mathematics
Yanbian University
Yanji, Jilin 133000, China
email: fangming@ybu.edu.cn

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