Research Article
The Existence of Countably Many Positive Solutions for Nonlinear ![]()
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
Boundary Value Problems 2009, 2009:572512 doi:10.1155/2009/572512
Published: 4 November 2009Abstract
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.
