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Complex Variables and Elliptic Equations
An International Journal
Volume 60, 2015 - Issue 12
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Articles

Radial symmetry and monotonicity for fractional Hénon equation in Rn

Pengyan WangCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007P.R. China.View further author information
,
Zhaohui DaiCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007P.R. China.Correspondence[email protected]
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&
Linfen CaoCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007P.R. China.View further author information
Pages 1685-1695 | Received 19 Nov 2014, Accepted 13 Apr 2015, Published online: 20 Jul 2015

References

  • Cao L, Chen W. Liouville type theorems for poly-harmonic Navier problems. Discrete Contin. Dyn. Syst. 2013;33:3937–3955.
  • Chen W, Li C. An integral system and the Lane--Emden conjecture. Discrete Contin. Dyn. Syst. 2009;24:1167–1184.
  • Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm. Pure Appl. Math. 2006;59:330–343.
  • Wei J, Xu X. Classification of solutions of higher order conformally invariant equations. Math. Ann. 1999;313:207–228.
  • Gidas B, Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 1981;34:525–598.
  • Phan QH, Souplet P. Liouville-type theorems and bounds of solutions of Hardy--Hénon equations. J. Diff. Equ. 2012;252:2544–2562.
  • Bogdan K, Kulczycki T, Nowak A. Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes. Illinois J. Math. 2002;46:541–556.
  • Caffarelli L, Vasseur A. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. 2010;171:1903–1930.
  • Chen W, Fang Y, Yang R. Loiuville theorems involving the fractional Laplacian on a half space. Adv. Math. 2015;274:167–198.
  • Chen W, D’Ambrosio L, Li Y. A new Liouville theorem for the fractional Laplacian. Nonl. Anal: Theory Methods Appl. Forthcoming. doi:10.1016/j.na.2014.11.003.
  • Chen W, Li C, Ou B. Qualitative properties of solutions for an integral equation. Discrete Contin. Dyn. Syst. 2005;12:347–354.
  • Constantin P. Navier--Stokes equations and turbulence. Mathematical foundation of turbulent viscous flows. Berlin: Springer; 2006. p. 1–43.
  • Serra E. Non radial positive solutions for the Hénon equation with critical growth. Calc. Var. 2005;23:301–326.
  • Tarasov VE, Zaslavsky G, George M. Fractional dynamics of systems with long-range interaction. Commun. Nonlinear Sci. Numer. Simul. 2006;11:885–898.
  • Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Commun. Pure Appl. Math. 2007;60:67–112.
  • Zhuo R, Chen W, Cui X, Yuan Z. A Liouville theorem for the fractional Laplacian. Discrete Contin. Dyn. Syst. Forthcoming. arXiv:1401.7402.
  • Kulczycki T. Properties of Green function of symmetry stable processes. Probab. Math. Statist. 1997;17:339–364.

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