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Radial and non-radial solutions for a class of (p, q)-Laplace equations involving weights

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  25 July 2025

Ky Ho Open the ORCID record for Ky Ho [Opens in a new window] ,
Kanishka Perera Open the ORCID record for Kanishka Perera [Opens in a new window]  and
Inbo Sim Open the ORCID record for Inbo Sim [Opens in a new window]
Ky Ho
Affiliation:
Institute of Applied Mathematics, University of Economics Ho Chi Minh City, 59C, Nguyen Dinh Chieu Street, District 3, Ho Chi Minh City, Vietnam (kyhn@ueh.edu.vn)
Kanishka Perera
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, United States (kperera@fit.edu)
Inbo Sim*
Affiliation:
Department of Mathematics, University of Ulsan, Ulsan, Republic of Korea (ibsim@ulsan.ac.kr) (corresponding author)
*
*Corresponding author.
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Abstract

We investigate radial and non-radial solutions to a class of (p, q)-Laplace equations involving weights. More precisely, we obtain existence and multiplicity results for nontrivial nonnegative radial and non-radial solutions, which extend results in the literature. Moreover, we study the non-radiality of minimizers in Hénon type (p, q)-Laplace problems and symmetry-breaking phenomena.

Dedicated to Professor Pavel Drábek on the occasion of his seventieth birthday

Keywords

non-radial solutionsvariational methodsweighted (p, q)-Laplacian

MSC classification

Primary: 35J92: Quasilinear elliptic equations with $p$-Laplacian
Secondary: 35J20: Variational methods for second-order elliptic equations 35B06: Symmetries, invariants, etc.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 33
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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