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Existence and uniqueness of positive solutions for some singular boundary value problems with linear functional boundary conditions

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Abstract

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0,1] positive solutions as well as the C 1[0, 1] positive solutions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P. R. China

    Zeng Qin Zhao & Fu Shan Li

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  1. Zeng Qin Zhao
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  2. Fu Shan Li
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Correspondence to Zeng Qin Zhao.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 10871116), Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AM005) and the Doctoral Program Foundation of Education Ministry of China (Grant No. 200804460001)

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Zhao, Z.Q., Li, F.S. Existence and uniqueness of positive solutions for some singular boundary value problems with linear functional boundary conditions. Acta. Math. Sin.-English Ser. 27, 2073–2084 (2011). https://doi.org/10.1007/s10114-011-8023-4

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  • DOI: https://doi.org/10.1007/s10114-011-8023-4

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