Open Access Research

Sign-changing solution for a third-order boundary-value problem in ordered Banach space with lattice structure

Xiuli Lin* and Zengqin Zhao

Author Affiliations

School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P.R. China

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Boundary Value Problems 2014, 2014:132  doi:10.1186/1687-2770-2014-132

Published: 22 May 2014

Abstract

In this paper, the sign-changing solution of a third-order two-point boundary-value problem is considered. By calculating the eigenvalues and the algebraic multiplicity of the linear problem and using a new fixed point theorem in an ordered Banach space with lattice structure, we give some conditions to guarantee the existence for a sign-changing solution.

Keywords:
third-order boundary-value problem; sign-changing solution; Green’s function; fixed point; lattice