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

This work is concerned with the existence of a second-order three-point boundary value problem on the half-line x" (t) + f (t, x (t), x' (t)) = 0, 0 < t < +infinity, x(0) = alpha x(eta), lim (t --> +infinity) x'(t) = 0, where alpha is an element of R, alpha not equal 1 and eta is an element of (0, +infinity) are given. After the discussion of the Green function for the corresponding homogeneous system on the half-line, we establish some criteria for the existence of solutions to the system discussed with suitable conditions imposed on f. The results are obtained by the Leray-Schauder continuation theorem. (C) 2005 Elsevier Ltd. All rights reserved.