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Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Dependence on Infinite Intervals

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Abstract

The existence of at least one positive solution and the existence of multiple positive solutions are established for the singular second-order boundary value problem

$$\left\{\begin{array}{l}{\frac{1}{p(t)}(p(t)x'(t))'}+\Phi(t)f(t,x,px')=0,\quad 0<t<+\infty,\\[2pt]x(0)=0,\quad \lim_{t\to+\infty}p(t)x'(t)=0\end{array}\right.$$

using the fixed point index, where f may be singular at x=0 and px′=0.

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Authors and Affiliations

  1. Department of Mathematics, Shandong Normal University, Ji-nan, 250014, China

    Baoqiang Yan

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

    Donal O’Regan

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

    Ravi P. Agarwal

Authors
  1. Baoqiang Yan
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  2. Donal O’Regan
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  3. Ravi P. Agarwal
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Corresponding author

Correspondence to Ravi P. Agarwal.

Additional information

The project is supported by the fund of National Natural Science (10571111) and the fund of Natural Science of Shandong Province.

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Yan, B., O’Regan, D. & Agarwal, R.P. Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Dependence on Infinite Intervals. Acta Appl Math 103, 19–57 (2008). https://doi.org/10.1007/s10440-008-9218-2

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  • DOI: https://doi.org/10.1007/s10440-008-9218-2

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