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

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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.

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The project is supported by the fund of natural science of Shandong Province.

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Yan, B., O’Regan, D. & Agarwal, R.P. Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative Dependence. Positivity 11, 687–720 (2007). https://doi.org/10.1007/s11117-007-2068-8

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