Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-LineReport as inadecuate




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Boundary Value Problems

, 2010:236560

Degenerate and Singular Differential Operators with Applications to Boundary Value Problems

Abstract

This paper investigates the second-order multipoint boundary value problem on the half-line Open image in new window,Open image in new window, Open image in new window, Open image in new window, Open image in new window, where Open image in new window, Open image in new window, Open image in new window, Open image in new window, and Open image in new window 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 Open image in new window 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.

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Author: Lishan Liu - Xinan Hao - Yonghong Wu

Source: https://link.springer.com/







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