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Solvability for second-order three-point boundary value problems at resonance on a half-line. (English) Zbl 1136.34034
Summary: This paper deals with the solvability and uniqueness of the second-order three-point boundary value problems at resonance on a half-line
$x''(t)=f(t,x(t),x'(t)),\quad 0<t<+\infty,$
$x(0)= x(\eta),\quad \lim_{t\to+\infty} x'(t)=0,$
and
$x''(t)=f(t,x(t),x'(t))+e(t),\quad 0<t<+\infty,$
$x(0)=x(\eta),\quad \lim_{t\to+\infty} x'(t)=0,$
where $$f:[0,+\infty]\times\mathbb R^2\to\mathbb R,$$ $$e:[0,+\infty]\to\mathbb R$$ are continuous and $$\eta\in (0,+\infty)$$. By using the coincidence degree theory, we establish some existence and uniqueness criteria.

##### MSC:
 34B40 Boundary value problems on infinite intervals for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
##### Keywords:
coincidence degree theory; infinite intervals
Full Text:
##### References:
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