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The ground states of quasilinear Hénon equation with double weighted critical exponents

Part of: Elliptic equations and systems Partial differential equations Close-to-elliptic equations and systems

Published online by Cambridge University Press:  03 June 2022

Cong Wang  and
Jiabao Su
Cong Wang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 100144, People's Republic of China ([email protected])
Jiabao Su
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing 100048, People's Republic of China ([email protected])
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Abstract

We prove the existence of nontrivial ground state solutions of the critical quasilinear Hénon equation $\displaystyle -\Delta _p u=|x|^{\alpha _1}|u|^{p^{*}(\alpha _1)-2}u-|x|^{\alpha _2}|u|^{p^{*}(\alpha _2)-2}u\ \ {\rm in}\ \mathbb {R}^{N}.$ It is a new problem in the sense that the signs of the coefficients of critical terms are opposite.

Keywords

Double weighted critical exponentsground statesvariational methods

MSC classification

Primary: 35B38: Critical points
Secondary: 35H30: Quasi-elliptic equations 35J75: Singular elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 3 , June 2023 , pp. 1037 - 1044
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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