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The existence of three positive solutions for some nonlinear boundary value problems on the half-line

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Abstract

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line

$$(\varphi(u^\prime))^\prime + a(t)f(t, u(t)) = 0, \quad 0 < t <+\infty,$$
$$u(0) = \sum_{i=1}^{m-2} \alpha_iu(\xi_i), \quad u^\prime(\infty) = 0,$$

where \({\varphi:}R {\rightarrow}R\) is the increasing homeomorphism and positive homomorphism and \(\varphi(0) =0\). We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term by using the five functionals fixed-point theorem.

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Authors and Affiliations

  1. Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, 210097, Jiangsu, P.R. China

    Sihua Liang & Jihui Zhang

  2. College of Mathematics, Changchun Normal University, Changchun, 130032, Jilin, P.R. China

    Sihua Liang

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  1. Sihua Liang
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  2. Jihui Zhang
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Correspondence to Sihua Liang.

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Project supported by Foundation of Major Project of Science and Technology of Chinese Education Ministry, SRFDP of Higher Education, NSF of Education Committee of Jiangsu Province and Project of Graduate Education Innovation of Jiangsu Province.

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Liang, S., Zhang, J. The existence of three positive solutions for some nonlinear boundary value problems on the half-line. Positivity 13, 443–457 (2009). https://doi.org/10.1007/s11117-008-2213-z

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  • DOI: https://doi.org/10.1007/s11117-008-2213-z

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