MATHEMATICA BOHEMICA, Vol. 136, No. 1, pp. 69-79, 2011

Positive solution to a singular $(k,n-k)$ conjugate boundary value problem

Qingliu Yao

Qingliu Yao, Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China, e-mail: yaoqingliu2002@hotmail.com

Abstract: The positive solution is studied for a $(k,n-k)$ conjugate boundary value problem. The nonlinear term is allowed to be singular with respect to both the time and space variables. By applying the approximation theorem for completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, an existence theorem for a positive solution is established.

Keywords: singular ordinary differential equation, higher order boundary value problem, positive solution, existence theorem

Classification (MSC 2010): 34B16, 34B18

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