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

Abstract

This paper deals with the solvability and uniqueness of the second-order three-point boundary value problems at resonance on a half-linex″ (t) = f (t, x (t), x′ (t)), 0 < t < + ∞,x (0) = x (η), under(lim, t → + ∞) x′ (t) = 0, andx″ (t) = f (t, x (t), x′ (t)) + e (t), 0 < t < + ∞,x (0) = x (η), under(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.