Open Access Research Article

Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line

Lishan Liu1,2*, Xinan Hao1 and Yonghong Wu2

Author Affiliations

1 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China

2 Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia

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Boundary Value Problems 2010, 2010:236560 doi:10.1155/2010/236560

Published: 18 October 2010

Abstract

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.