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Existence of positive solutions for \(n\)th-order singular sublinear boundary value problems with all derivatives

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Abstract

This paper investigates the existence of positive solutions for \(n\)th-order (\(n\ge 3\)) singular sub-linear boundary value problems with all derivatives. A necessary and sufficient condition for the existence of \(C^{n-1}[0,1]\) positive solutions is given by constructing lower and upper solutions and with the comparison theorem. Our nonlinearity \(f(t,x_1,x_2,\ldots ,x_n)\) may be singular at \(x_i=0,\ i=1, \ 2,\ \ldots ,\ n, \ t=0\) and /or \(t=1\).

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Acknowledgments

The authors are grateful to the referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Shandong Jianzhu University, Jinan , 250101, Shandong, People’s Republic of China

    Zhongli Wei

  2. School of Mathematics and System Sciences, Shandong University, Jinan , 250100, Shandong, People’s Republic of China

    Zhongli Wei

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  1. Zhongli Wei
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Correspondence to Zhongli Wei.

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Research supported by the NSF of Shandong Province (ZR2013AM009).

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Wei, Z. Existence of positive solutions for \(n\)th-order singular sublinear boundary value problems with all derivatives. J. Appl. Math. Comput. 48, 41–54 (2015). https://doi.org/10.1007/s12190-014-0790-5

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  • DOI: https://doi.org/10.1007/s12190-014-0790-5

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