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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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The Lane-Emden equation with variable double-phase and multiple regime
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by Claudianor O. Alves and Vicenţiu D. Rădulescu PDF
Proc. Amer. Math. Soc. 148 (2020), 2937-2952 Request permission


We are concerned with the study of the Lane-Emden equation with variable exponent and Dirichlet boundary condition. The feature of this paper is that the analysis that we develop does not assume any subcritical hypotheses and the reaction can fulfill a mixed regime (subcritical, critical, and supercritical). We consider the radial and the nonradial cases, as well as a singular setting. The proofs combine variational and analytic methods with a version of the Palais principle of symmetric criticality.
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Additional Information
  • Claudianor O. Alves
  • Affiliation: Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande - PB, Brazil
  • MR Author ID: 610236
  • Email:
  • Vicenţiu D. Rădulescu
  • Affiliation: Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland; and Department of Mathematics, University of Craiova, 200585 Craiova, Romania; and Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589, Saudi Arabia
  • MR Author ID: 143765
  • ORCID: 0000-0003-4615-5537
  • Email:
  • Received by editor(s): November 11, 2019
  • Published electronically: April 9, 2020
  • Communicated by: Catherine Sulem
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2937-2952
  • MSC (2010): Primary 35J20; Secondary 35J75, 35J92, 35P30
  • DOI:
  • MathSciNet review: 4099782