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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)),0<t<+,
x(0)=x(η),lim t+ x ' (t)=0,

and

x '' (t)=f(t,x(t),x ' (t))+e(t),0<t<+,
x(0)=x(η),lim t+ x ' (t)=0,

where f:[0,+]× 2 , e:[0,+] are continuous and η(0,+). By using the coincidence degree theory, we establish some existence and uniqueness criteria.

MSC:
34B40Boundary value problems for ODE on infinite intervals
34B10Nonlocal and multipoint boundary value problems for ODE
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