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Singular Solutions of Elliptic Equations with Iterated Exponentials

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Abstract

We construct positive singular solutions for the problem \(-\Delta u=\lambda \exp (e^u)\) in \(B_1\subset {\mathbb {R}}^n\) (\(n\ge 3\)), \(u=0\) on \(\partial B_1\), having a prescribed behaviour around the origin. Our study extends the one in Miyamoto (J Differ Equ 264:2684–2707, 2018) for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials.

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Authors and Affiliations

  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Marius Ghergu

  2. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

    Marius Ghergu

  3. Laboratoire Amiénois de Mathématiques Fondamentales et Appliquée, (LAMFA UMR 7352 CNRS UPJV), Université de Picardie Jules Verne, 33 rue saint-Leu, 80039, Amiens, France

    Olivier Goubet

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  1. Marius Ghergu
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  2. Olivier Goubet
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Correspondence to Marius Ghergu.

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Ghergu, M., Goubet, O. Singular Solutions of Elliptic Equations with Iterated Exponentials. J Geom Anal 30, 1755–1773 (2020). https://doi.org/10.1007/s12220-019-00277-1

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