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2021 Finite Morse Index Solutions of the Fractional Henon–Lane–Emden Equation with Hardy Potential
Soojung Kim, Youngae Lee
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Taiwanese J. Math. Advance Publication 1-33 (2021). DOI: 10.11650/tjm/211203

Abstract

In this paper, we study the fractional Henon–Lane–Emden equation associated with Hardy potential \[ (-\Delta)^{s} u - \gamma |x|^{-2s} u = |x|^a |u|^{p-1} u \quad \textrm{in $\mathbb{R}^{n}$}. \] Extending the celebrated result of [14], we obtain a classification result on finite Morse index solutions to the fractional elliptic equation above with Hardy potential. In particular, a critical exponent $p$ of Joseph–Lundgren type is derived in the supercritical case studying a Liouville type result for the $s$-harmonic extension problem.

Funding Statement

S. Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (No. NRF-2018R1C1B6003051). Y. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2018R1C1B6003403).

Acknowledgments

The authors would like to thank Prof. Jinmyoung Seok for helpful discussions.

Citation

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Soojung Kim. Youngae Lee. "Finite Morse Index Solutions of the Fractional Henon–Lane–Emden Equation with Hardy Potential." Taiwanese J. Math. Advance Publication 1 - 33, 2021. https://doi.org/10.11650/tjm/211203

Information

Published: 2021
First available in Project Euclid: 19 December 2021

Digital Object Identifier: 10.11650/tjm/211203

Subjects:
Primary: 35B33, 35B35, 35B45, 35B53, 35B65

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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