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June, 2021 Symmetry of Positive Solutions to Quasilinear Fractional Systems
Phuong Le
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Taiwanese J. Math. 25(3): 517-534 (June, 2021). DOI: 10.11650/tjm/201203

Abstract

Using the method of moving planes, we establish the radial symmetry of positive solutions to the fractional system \[ \begin{cases} (-\Delta)^s_p u = f(u,v), \\ (-\Delta)^t_q v = g(u,v) \end{cases} \] in the entire Euclidean space $\mathbb{R}^n$ and in the unit ball, where $0 \lt s,t \lt 1$ and $p,q \geq 2$. In particular, our result can be applied to the nonlinearities $f(u,v) \equiv u^a v^b$ and $g(u,v) \equiv u^c v^d$, where $a,d \in \mathbb{R}$ and $b,c \gt 0$.

Citation

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Phuong Le. "Symmetry of Positive Solutions to Quasilinear Fractional Systems." Taiwanese J. Math. 25 (3) 517 - 534, June, 2021. https://doi.org/10.11650/tjm/201203

Information

Received: 24 April 2020; Accepted: 3 December 2020; Published: June, 2021
First available in Project Euclid: 11 December 2020

Digital Object Identifier: 10.11650/tjm/201203

Subjects:
Primary: 35B06, 35J92, 35R11

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

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Vol.25 • No. 3 • June, 2021
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