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Nonnegative solutions of an elliptic equation with a singular potential

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Abstract

We study the behavior of nonnegative solutions of the Dirichlet problem for a linear elliptic equation with a singular potential in the ball B = B(0,R) ⊂ R n (n ≥ 3), R ≤ 1. We find an exact condition on the potential ensuring the existence or absence of a nonnegative solution of that problem.

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Authors and Affiliations

  1. Turkmen State University, Ashgabat, Turkmenistan

    B. A. Khudaigulyev

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  1. B. A. Khudaigulyev
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Original Russian Text © B.A. Khudaigulyev, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 2, pp. 246–254.

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Khudaigulyev, B.A. Nonnegative solutions of an elliptic equation with a singular potential. Diff Equat 48, 255–263 (2012). https://doi.org/10.1134/S0012266112020097

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  • DOI: https://doi.org/10.1134/S0012266112020097

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