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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,327 - 1,345 (19page)
- DOI
- 10.4134/JKMS.j200616
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초록· 키워드
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In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type \begin{equation*} u(x)=\overrightarrow{l}+C_{*}\int_{\mathbb{R}^n}\frac{(1-|u(y)|^2)|u(y)|^2u(y)-\frac{1}{2}(1-|u(y)|^2)^2u(y)}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:\mathbb{R}^n\rightarrow \mathbb{R}^k$ is a bounded, uniformly continuous function with $k\geqslant1$ and $0<\alpha<n$,$\overrightarrow{l}\in \mathbb{R}^k$ is a constant vector, and $C_{*}$ is a real constant. We prove that $|\overrightarrow{l}|\in \{0,\frac{\sqrt{3}}{3},1\}$ if $u$ is the finite energy solution. Further, if $u$ is also a differentiable solution, then we give a Liouville type theorem, that is either $u\rightarrow\overrightarrow{l}$ with $|\overrightarrow{l}|=\frac{\sqrt{3}}{3}$, when $|x|\rightarrow \infty$, or $u\equiv\overrightarrow{l},$ where $|\overrightarrow{l}|\in \{0,1\}.$
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참고문헌 (13)
참고문헌 신청
K. Bogdan / 2002 / Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes / Illinois J. Math 46(2):541~556
H. Brezis / 1994 / Quantization effects for Δu = u(1 - lul²) in R² / Arch. Rational Mech. Anal 126(1):35~58
Jongmin Han / 2010 / Quantization effects for Maxwell–Chern–Simons vortices / Journal of Mathematical Analysis and Applications 363(1):265~274
Jongmin Han / 2008 / On the Chern–Simons–Higgs vortex equation without gauge fields / Nonlinear Analysis: Theory, Methods & Applications 69(9):2950~2963
Jongmin Han / 2005 / Nonself-dual Chern–Simons and Maxwell–Chern–Simons vortices on bounded domains / Journal of Functional Analysis 221(1):167~204
H. Brezis / 1994 / Quantization effects for Δu = u(1 - lul²) in R² / Arch. Rational Mech. Anal 126(1):35~58
Jongmin Han / 2010 / Quantization effects for Maxwell–Chern–Simons vortices / Journal of Mathematical Analysis and Applications 363(1):265~274
Jongmin Han / 2008 / On the Chern–Simons–Higgs vortex equation without gauge fields / Nonlinear Analysis: Theory, Methods & Applications 69(9):2950~2963
Jongmin Han / 2005 / Nonself-dual Chern–Simons and Maxwell–Chern–Simons vortices on bounded domains / Journal of Functional Analysis 221(1):167~204
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