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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,449 - 1,460 (12page)
- DOI
- 10.4134/JKMS.j210091
이용수
초록· 키워드
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In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity $$ (-\Delta)^{s}u(x)=\lambda u^{\beta}(x)+a_{0}u^{-\gamma}(x), ~ x\in \mathbb{R}^{n}, $$ where $0<s<1$, $\gamma>0$, $1<\beta\leq\frac{n+2s}{n-2s}$, $\lambda>0$ are constants and $a_{0}\geq0$. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions $u(x)$ must be radially symmetric and monotone increasing about some point in $\mathbb{R}^{n}$.
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참고문헌 (12)
참고문헌 신청
A. L. Bertozzi / 1998 / Long-wave instabilities and saturation in thin film equations / Comm. Pure Appl. Math 51(6):625~661
C. Brändle / 2013 / A concave—convex elliptic problem involving the fractional Laplacian / Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143(1):39~71
Luis A. Caffarelli / 2008 / Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian / Inventiones mathematicae 171(2):425~461
Luis Caffarelli / 2007 / An Extension Problem Related to the Fractional Laplacian / Communications in Partial Differential Equations 32(8):1245~1260
Luis Caffarelli / 2009 / Regularity theory for fully nonlinear integro-differential equations / Communications on Pure and Applied Mathematics 62(5):597~638
C. Brändle / 2013 / A concave—convex elliptic problem involving the fractional Laplacian / Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143(1):39~71
Luis A. Caffarelli / 2008 / Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian / Inventiones mathematicae 171(2):425~461
Luis Caffarelli / 2007 / An Extension Problem Related to the Fractional Laplacian / Communications in Partial Differential Equations 32(8):1245~1260
Luis Caffarelli / 2009 / Regularity theory for fully nonlinear integro-differential equations / Communications on Pure and Applied Mathematics 62(5):597~638
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