Solvability for second-order three-point boundary value problems at resonance on a half-line ✩

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,+∞) × R2 →R, e : [0,+∞)→R are continuous and η ∈ (0,+∞). By using the coincidence degree theory, we establish some existence and uniqueness criteria. © 2007 Elsevier Inc. All rights reserved.