Research Article
Exact Multiplicity of Positive Solutions for a Class of Second-Order Two-Point Boundary Problems with Weight Function
1 Department of Mathematics, Shanghai Institute of Technology, Shanghai 200235, China
2 School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China
Boundary Value Problems 2010, 2010:207649 doi:10.1155/2010/207649
Published: 17 August 2010Abstract
An exact multiplicity result of positive solutions for the boundary value problems
, 
, 
, 
is achieved, where 
is a positive parameter. Here the function 
is 
and satisfies 
, 
for 
for some 
. Moreover, 
is asymptotically linear and 
can change sign only once. The weight function 
is 
and satisfies 
, 
for 
. Using bifurcation techniques, we obtain the exact number of positive solutions of
the problem under consideration for 
lying in various intervals in 
. Moreover, we indicate how to extend the result to the general case.
