| [1] |
Berestycki H, Nirenberg L. On the method of moving planes and the sliding method. Bol Soc Brasil Mat (NS), 1991, 22(1): 1-37
|
| [2] |
Chen W, Hu Y. Monotonicity of positive solutions for nonlocal problems in unbounded domains. J Funct Anal, 2021, 281(9): 109187
doi: 10.1016/j.jfa.2021.109187
|
| [3] |
Chen W, Li C. Classification of solutions of some nonlinear elliptic equations. Duke Math J, 1991, 63(3): 615-622
|
| [4] |
Chen W, Li C, Li Y. A direct method of moving planes for the fractional Laplacian. Adv Math, 2017, 308: 404-437
doi: 10.1016/j.aim.2016.11.038
|
| [5] |
Chen W, Li Y, Ma P. The Fractional Laplacian. Hackensack: World Scientific, 2020
|
| [6] |
Chen W, Li Y, Zhang R. A direct method of moving spheres on fractional order equations. J Funct Anal, 2017, 272(10): 4131-4157
doi: 10.1016/j.jfa.2017.02.022
|
| [7] |
Chen W, Wu L. A maximum principle on unbounded domains and a Liouville theorem for fractional $p$-harmonic functions. arXiv:1905.09986
|
| [8] |
Chen W, Wang P, Niu Y, Hu Y. Asymptotic method of moving planes for fractional parabolic equations. Adv Math, 2021, 377: 107463
doi: 10.1016/j.aim.2020.107463
|
| [9] |
Chen W, Wu L. Liouville theorems for fractional parabolic equations. Adv Nonlinear Stud, 2021, 21(4): 939-958
|
| [10] |
Du L, Tang Y. The steady incompressible jet flows issuing from a finitely long nozzle. Journal of Differential Equations, 2021, 280: 355-374
|
| [11] |
Fernández-Real X, Ros-Oton X. Regularity theory for general stable operators: Parabolic equations. J Funct Anal, 2017, 272(10): 4165-4221
|
| [12] |
Geng S, Tang Y. Convergence rates to nonlinear diffusive waves for solutions to nonlinear hyperbolic system. Acta Mathematica Scientia, 2019, 39B(1): 46-56
|
| [13] |
Hamel F, Nadirashvili N. Entire solutions of the KPP equation. Comm Pure Appl Math, 1999, 52(10): 1255-1276
|
| [14] |
Hamel F, Nadirashvili N. Travelling fronts and entire solutions of the Fisher-KPP equation in $R^{N}$. Arch Ration Mech Anal, 2001, 157(2): 91-163
|
| [15] |
Li C. Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on bounded domains. Commun Partial Differ Equ, 1991, 16: 491-526
|
| [16] |
Li C. Some Qualitative Properties of Fully Nonlinear Elliptic and Parabolic Equations. New York: New York University, 1989
|
| [17] |
Li Y, Zhu M. Uniqueness theorems through the method of moving spheres. Duke Math J, 1995, 80(2): 383-417
|
| [18] |
Liu Z, Chen W. Maximum principles and monotonicity of solutions for fractional $p$-equations in unbounded domains. arXiv: 1905.06493
|
| [19] |
Pol$\acute{\rm a}\check{\rm c}$ik P. Estimates of solutions and asymptotic symmetry for parabolic equations on unbounded domains. Arch Ration Mech Anal, 2007, 183: 59-91
|
| [20] |
Pol$\acute{\rm a}\check{\rm c}$ik P. Symmetry properties of positive solutions of parabolic equations on $R^{N},$ I: Asymptotic symmetry for the Cauchy problem. Commun Partial Differ Equ, 2005, 30: 1567-1593
|
| [21] |
武乐云, 陈文雄. 具 De Giorgi 型非线性分数阶方程解的单调性. 中国科学: 数学, 2022, 52(1): 1-22
|
|
Wu L Y, Chen W X. Monotonicity of solutions for fractional equations with De Giorgi type nonlinearities. Sci Sin Math, 2022, 52(1): 1-22
|
| [22] |
Wu L Y, Chen W X. The sliding methods for the fractional $p$-Laplacian. Adv Math, 2020, 361: Article ID 106933
|
| [23] |
Wu L Y, Chen W X. Ancient solutions to nonlocal parabolic equations. Advances in Mathematics, 2022, 408: 108607
|
| [24] |
Zhang B, Lü Z. Symmetry and nonexistence of solutions for a fully nonlinear nonlocal system. Pac J Math, 2019, 299: 237-255
|
