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Multiple positive solutions of singular dirichlet second-order boundary-value problems with derivative dependence

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Abstract

The existence of multiple positive solutions for the singular Dirichlet boundary-value problem

$$\begin{array}{*{20}c} {{x^{{\prime \prime }} + \Phi {\left( t \right)}f{\left( {t,x{\left( t \right)},x^{\prime } {\left( t \right)}} \right)} = 0,\,\,\,\,0 < t < 1,}} \\ {{x{\left( 0 \right)} = 0,x{\left( 1 \right)} = 0,}} \\ \end{array} $$

is presented by using the fixed point index; here f may be singular at x = 0.

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Authors and Affiliations

  1. Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida, 32901, USA

    Ravi P. Agarwal

  2. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  3. Department of Mathematics, Shandong Normal University, Ji-nan, 250014, P.R. China

    Baoqiang Yan

Authors
  1. Ravi P. Agarwal
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  2. Donal O’Regan
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  3. Baoqiang Yan
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Correspondence to Ravi P. Agarwal.

Additional information

This work was partially supported by the Foundation of Natural Science of Shandong Province.

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Agarwal, R.P., O’Regan, D. & Yan, B. Multiple positive solutions of singular dirichlet second-order boundary-value problems with derivative dependence. J Dyn Control Syst 15, 1–26 (2009). https://doi.org/10.1007/s10883-008-9060-x

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  • DOI: https://doi.org/10.1007/s10883-008-9060-x

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