Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function
Received:May 24, 2012  Revised:September 03, 2012
Key Word: singular ordinary differential equation   Sturm-Liouville boundary value problem   positive solution   existence and multiplicity.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11071109).
Author NameAffiliation
Qingliu YAO Department of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210003, P. R. China 
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      The existence and multiplicity of positive solutions are studied for a singular Sturm-Liouville boundary value problem with positive Green function, where the nonlinearity may be super-strongly singular with respect to the space variable. By constructing suitable control functions, the a priori bound of solution is exactly estimated. By applying the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several existence results are proved.
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