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The Lane-Emden equation with variable double-phase and multiple regime

Authors: Claudianor O. Alves and Vicenţiu D. Rădulescu
Journal: Proc. Amer. Math. Soc. 148 (2020), 2937-2952
MSC (2010): Primary 35J20; Secondary 35J75, 35J92, 35P30
Published electronically: April 9, 2020
MathSciNet review: 4099782
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Abstract: 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

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

Keywords: Lane-Emden equation, double-phase energy, variable exponent, nonhomogeneous differential operator, Palais principle of symmetric criticality
Received by editor(s): November 11, 2019
Published electronically: April 9, 2020
Communicated by: Catherine Sulem
Article copyright: © Copyright 2020 American Mathematical Society