Open Access Research Article

The Existence of Countably Many Positive Solutions for Nonlinear th-Order Three-Point Boundary Value Problems

Yude Ji* and Yanping Guo

Author Affiliations

College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

For all author emails, please log on.

Boundary Value Problems 2009, 2009:572512  doi:10.1155/2009/572512

Published: 4 November 2009

Abstract

We consider the existence of countably many positive solutions for nonlinear th-order three-point boundary value problem , , , , , where , for some and has countably many singularities in . The associated Green's function for the th-order three-point boundary value problem is first given, and growth conditions are imposed on nonlinearity which yield the existence of countably many positive solutions by using the Krasnosel'skii fixed point theorem and Leggett-Williams fixed point theorem for operators on a cone.