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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization for elliptic problems on fractal sets
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by Giovanni Molica Bisci and Vicenţiu D. Rădulescu PDF
Proc. Amer. Math. Soc. 143 (2015), 2959-2968 Request permission


In this paper we prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpiński gasket. More generally, the validity of our result can be checked studying elliptic equations defined on self-similar fractal domains whose spectral dimension $\nu \in (0,2)$. Our theorem can be viewed as an elliptic version on fractal domains of a recent contribution obtained in a recent work of Ricceri for a two-point boundary value problem.
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Additional Information
  • Giovanni Molica Bisci
  • Affiliation: Patrimonio, Architettura e Urbanistica, Department, University of Reggio Calabria, 89124 - Reggio Calabria, Italy
  • Email:
  • Vicenţiu D. Rădulescu
  • Affiliation: Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • MR Author ID: 143765
  • ORCID: 0000-0003-4615-5537
  • Email:
  • Received by editor(s): December 27, 2013
  • Received by editor(s) in revised form: February 3, 2014, and February 9, 2014
  • Published electronically: February 13, 2015
  • Communicated by: Catherine Sulem
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 2959-2968
  • MSC (2010): Primary 35J20; Secondary 28A80, 35J25, 35J60, 47J30, 49J52
  • DOI:
  • MathSciNet review: 3336620