Szczegóły obiektu: Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit

Instytucja dostarczająca:Akademicka Platforma Czasopism

Opis

Title:
Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit
Creator:
Feng, Zhenping;
Du, Zhuoran
Description:
We are concerned with periodic solutions of the fractional Laplace equation \begin{equation*} {(-\partial_{xx})^s}u(x)+F'(u(x))=0 \quad \mbox{in }\mathbb{R}, \end{equation*} where $0< s< 1$. The smooth function $F$ is a double-well potential with wells at $+1$ and $-1$. We show that the value of least positive period is $2{\pi}\times({1}/{-F''(0)})^{{1}/({2s})}$. The axial symmetry of odd periodic solutions is obtained by moving plane method. We also prove that odd periodic solutions $u_{T}(x)$ converge to a layer solution of the same equation as periods $T\rightarrow+\infty$.
Object availability:
Dostęp otwarty
Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
Prawa autorskie (c) 2022 Zhenping Feng, Zhuoran Du
Date:
2022.12.10
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
angielski
Source:
Topological Methods in Nonlinear Analysis; Vol 60, No 2 (December 2022); 633 - 651;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/41318/34039 ;https://apcz.umk.pl/TMNA/article/view/41318/34040
Subject:
Periodic solutions;
fractional Laplacian;
least positive period;
axial symmetry;
layer solution;
Primary: 54C40, 14E20;
Secondary: 46E25, 20C20
Identifier: https://apcz.umk.pl/TMNA/article/view/41318
Data provider:
Akademicka Platforma Czasopism

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Szczegóły obiektu: Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit

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