Copyright © 2010 Lishan Liu et al. This is an open access article distributed under the
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This paper investigates the second-order multipoint boundary value problem on the half-line ,, , , , where , , , , and
is continuous. We establish sufficient conditions to guarantee the existence of unbounded solution in a special function space by using nonlinear alternative of Leray-Schauder type. Under the condition that is nonnegative, the existence and uniqueness of unbounded positive solution are obtained based upon the fixed point index theory and Banach contraction mapping principle. Examples are also given to illustrate the main results.