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Zbl 1123.34307
Lian, Hairong; Ge, Weigao
Solvability for second-order three-point boundary value problems on a half-line.
(English)
[J] Appl. Math. Lett. 19, No. 10, 1000-1006 (2006). ISSN 0893-9659

Summary: This work is concerned with the existence of a solution to the second-order three-point boundary value problem on the half-line $$\cases x''(t)+f(t,x(t), x'(t))=0,\ 0<t<+\infty,\\ x(0)=\alpha x(\eta),\ \lim_{t\to+\infty}x'(t)=0, \endcases$$ where $\alpha\in \bbfR$, $\alpha\ne 1$ and $\eta\in(0,+\infty)$ are given. After the discussion of the Green function for the corresponding homogeneous system on the half-line, we establish some criteria for the existence of solutions to the system discussed with suitable conditions imposed on $f$. The results are obtained by the Leray-Schauder continuation theorem.
MSC 2000:
*34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE
34B40 Boundary value problems on infinite intervals

Keywords: three-point boundary value problem; Green function; Leray-Schauder continuation theorem

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