Open Access Research

Multiple unbounded solutions for a boundary value problem on infinite intervals

Hairong Lian* and Fengjie Geng

Author Affiliations

School of Information Engineering, China University of Geoscience, Beijing 100083, People's Republic of China

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Boundary Value Problems 2011, 2011:51  doi:10.1186/1687-2770-2011-51

Published: 30 November 2011

Abstract

This paper is concerned with the existence of multiple unbounded solutions for a Sturm-Liouville boundary value problem on the half-line. By assuming the existence of two pairs of unbounded upper and lower solutions, the existence of at least three solutions is obtained using the degree theories. Nagumo condition plays an important role in the nonlinear term involved in the first-order derivative. It is an interesting point that the method of unbounded upper and lower solutions is extended to obtain conditions for the existence of multiple solutions.

Mathematics Subject Classification (2000 34B10, 34B40

Keywords:
infinite interval problem; multiplicity; unbounded upper solutions; unbounded lower solutions; degree theory