Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function

Abstract:

      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.