Singular Solutions of Elliptic Equations with Iterated Exponentials

  • Marius GherguEmail author
  • Olivier Goubet


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.


Singular solutions Prescribed singularity Iterated exponentials 

Mathematics Subject Classification

Primary 35J61 35J75 Secondary 35B40 



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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.School of Mathematics and StatisticsUniversity College DublinDublin 4Ireland
  3. 3.Laboratoire Amiénois de Mathématiques Fondamentales et Appliquée, (LAMFA UMR 7352 CNRS UPJV)Université de Picardie Jules VerneAmiensFrance

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