The Existence of Countably Many Positive Solutions for Nonlinear
th-Order Three-Point Boundary Value Problems !()
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
Boundary Value Problems 2009, 2009:572512 doi:10.1155/2009/572512Published: 4 November 2009
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.