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Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence

Authors:

Baoqiang Yan Donal O’Regan Ravi P Agarwal

Institution:

(1) Department of Mathematics, Shandong Normal University, Ji-nan, 250014, P.R. China;(2) Department of Mathematics, National University of Ireland, Galway, Ireland;(3) Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA

Abstract:

The existence of multiple positive solutions is presented for the singular second-order boundary value problems

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

using the fixed point index, where f may be singular at x = 0 and x′ = 0. The project is supported by the fund of natural science of Shandong Province.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 34B15 34B16 34B17

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