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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
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