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Multiplicity of Solutions of Dirichlet Second Order Boundary Value Problems with Derivative Dependance

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Abstract

In this paper we present some theorems on the multiplicity of fixed points of some operators on a special wedge and using these results we consider

$$\begin{aligned} \left\{ \begin{array}{ll} x^{\prime \prime }+f(t,x, x') =0,\,\,\,t\in (0,1)\\ x(0) =0,\,\,\,x(1) =0\\ \end{array} \right. \end{aligned}$$

and establish the existence of multiple solutions.

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Acknowledgements

We are thankful to the support of the National Natural Science Foundation of China and the Fund of Natural Science of Shandong Province. The authors were supported by the NSFSP (ZR2018MA022) and the NSFC (61603226).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China

    Baoqiang Yan

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  3. Department of Mathematics, Texas A and M University-Kingsville, Kingsville, TX, 78363, USA

    Ravi P. Agarwal

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  1. Baoqiang Yan
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  2. Donal O’Regan
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  3. Ravi P. Agarwal
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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to Baoqiang Yan.

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Yan, B., O’Regan, D. & Agarwal, R.P. Multiplicity of Solutions of Dirichlet Second Order Boundary Value Problems with Derivative Dependance. Differ Equ Dyn Syst 31, 805–826 (2023). https://doi.org/10.1007/s12591-020-00535-7

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