Pengyan WANG
,
Yongzhong WANG
. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM[J]. Acta mathematica scientia, Series B, 2018
, 38(3)
: 935
-949
.
DOI: 10.1016/S0252-9602(18)30794-X
[1] Bouchard J, Georges A. Anomalous diffusion in disordered media, Statistical mechanics, models and physical applications. Phys Rep, 1990, 195:127-293
[2] Caffarelli L, Silvestre L. Regularity theory for fully nonlinear integro-differential equations. Comm Pure Appl Math, 2009, 62:597-638
[3] Caffarelli L, Silvestre L. Regularity results for nonlocal equations by approximation. Arch Ration Mech Anal, 2011, 200:59-88
[4] Caffarelli L, Silvestre L. An extension problem related to the fractonal Laplacian. Comm PDE, 2007, 32:1245-1260
[5] Caffarelli L, Vasseur L. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann Math, 2010, 171:1903-1930
[6] Chen W, Li C, Li G. Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions. Calc Var Partial Differential Equations, 2017, 56:29
[7] Chen W, Li C, Li Y. A drirect method of moving planes for the fractional Laplacian. Adv Math, 2017, 308:404-437
[8] Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math, 2006, 59:330-343
[9] Constantin P. Euler equations, Navier-Stokes equations and turbulence//Mathematical foundation of turbulent viscous flows. Lecture Notes in Math, 2006, 1871:1-43
[10] Jarohs S, Weth T. Symmetry via antisymmetric maximum principle in nonlocal problems of variable order. Ann Mat Pura Appl, 2016, 195:273-291
[11] Li Y, Ma P. Symmetry of solutions for a fractional system. Sci China Math, 2017:1-20
[12] Lei Y, Li C, Ma C. Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations. Calc Var Partial Differential Equations, 2012, 45:43-61
[13] Ma L, Chen D. A Liouville type Theorem for an integral system. Comm Pure Appl Anal, 2006, 5:855-859
[14] Ma L, Liu B. Radial symmetry results for fractional Laplacian systems. Nonlinear Anal, 2016, 146:120-135
[15] Tang D. Positive solutions to semilinear elliptic equations involving a weighted fractional Laplacian. Math Methods Appl Sci, doi:10.1002/mma.4184
[16] Wang P, Yu M. Solutions of fully nonlinear nonlocal systems. J Math Anal Appl, 2017, 450:982-995
[17] Zhuo R, Chen W, Cui X, Yuan Z. Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian. Discrete Contin Dyn Syst, 2016, 36:1125-1141
