New Fixed Point Theorems of Mixed Monotone Operators and Applications to Singular Boundary Value Problems on Time Scales
College of Economics and Management, North University of China, Taiyuan, Shanxi 030051, China
Boundary Value Problems 2011, 2011:567054 doi:10.1155/2011/567054Published: 21 December 2010
Some new existence and uniqueness theorems of fixed points of mixed monotone operators are obtained, and then they are applied to a nonlinear singular second-order three-point boundary value problem on time scales. We prove the existence and uniqueness of a positive solution for the above problem which cannot be solved by using previously available methods.