[1] Cao D, Dai W, Qin G, et al. Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians. Transactions of the American Mathematical Society, 2021, 374(7): 4781-4813 [2] Chen W, Li C, Ou B, et al. Qualitative properties of solutions for an integral equation. Discrete & Continuous Dynamical Systems, 2005, 12(2): 347 [3] Chen W, Li C, Li Y, et al. A direct method of moving planes for the fractional Laplacian. Advances in Mathematics, 2017, 308: 404-437 [4] Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 2007, 60(1): 67-112 [5] Chen W, Li C, Ou B, et al. Classification of solutions for an integral equation. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 2006, 59(3): 330-343 [6] Wei J, Xu X. Classification of solutions of higher order conformally invariant equations. Mathematische Annalen, 1999, 313(2): 207-228 [7] Chen W, Li C. Super polyharmonic property of solutions for PDE systems and its applications. Communications on Pure & Applied Analysis, 2013, 12(6): 2497 [8] Fang Y, Chen W. A Liouville type theorem for poly-harmonic Dirichlet problems in a half space. Advances in Mathematics, 2012, 229(5): 2835-2867 [9] Chen W, Fang Y, Li C, et al. Super poly-harmonic property of solutions for Navier boundary problems on a half space. Journal of Functional Analysis, 2013, 265(8): 1522-1555 [10] Dai W, Liu Z, Qin G L. Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell type equations. SIAM Journal on Mathematical Analysis, 2021, 53(2): 1379-1410 [11] Cheng T, Liu S. A Liouville type theorem for higher order Hardy-H'enon equation in $\mathbb{R}^n$. Journal of Mathematical Analysis and Applications, 2016, 444(1): 370-389 [12] Zhuo R, Li Y. A Liouville theorem for the higher-order fractional Laplacian. Communications in Contemporary Mathematics, 2019, 21(2): 1850005 [13] Cheng C, Lü Z, Lü Y, et al. A direct method of moving planes for the system of the fractional Laplacian. Pacific Journal of Mathematics, 2017, 290(2): 301-320 [14] Zhuo R, Li C. Classification of anti-symmetric solutions to nonlinear fractional Laplace equations. Calculus of Variations and Partial Differential Equations, 2022, 61(1): 1-23 [15] Zhuo R. Weighted polyharmonic equation with Navier boundary conditions in a half space. Science China Mathematics, 2017, 60(3): 491-510 [16] Li C, Liu C, Wu Z, Xu H, et al. Non-negative solutions to fractional Laplace equations with isolated singularity. Advances in Mathematics, 2020, 373: 107329 [17] Le P. Classification of solutions to higher fractional order systems. Acta Mathematica Scientia, 2021, 41B(4): 1302-1320 [18] Guo Q, Zhao L. Positive solutions with high energy for fractional Schrödinger equations. Acta Mathematica Scientia, 2023, 43B(4): 1116-1130 [19] Li G, Yang T. The existence of a nontrivial weak solution to a double critical problem involving a fractional Laplacian in $\mathbb{R}^N$ with a Hardy term. Acta Mathematica Scientia, 2020, 40B(6): 1808-1830 [20] Jiang C, Liu Z, Zhou L, et al. Blow-up in a fractional Laplacian mutualistic model with Neumann boundary conditions. Acta Mathematica Scientia, 2022, 42B(5): 1809-1816 [21] Wang P, Niu P. A priori bounds and the existence of positive solutions for weighted fractional systems. Acta Mathematica Scientia, 2021, 41B(5): 1547-1568 [22] Moussaoui A, Velin J. Existence and boundedness of solutions for systems of quasilinear elliptic equations. Acta Mathematica Scientia, 2021, 41B(2): 397-412 [23] Nyamoradi N, Razani A. Existence to fractional critical equation with Hardy-Littlewood-Sobolev nonlinearities. Acta Mathematica Scientia, 2021, 41B(4): 1321-1332 [24] Chen Y, Wei L, Zhang Y, et al. The asymptotic behavior and symmerty of positive solutions to $p$-Lapalcian equations in a half-space. Acta Mathematica Scientia, 2022, 42B(5): 2149-2164 [25] Bucur C. Some observations on the Green function for the ball in the fractional Laplace framework. Communications on Pure and Applied Analysis, 2016, 15(2): 657-699 [26] Stein E M.Singular Integrals and Differentiability Properties of Functions (PMS-30), Princeton: Princeton University Press, 2016 [27] Zhuo R, Chen W, Cui X, et al.A Liouville theorem for the fractional Laplacian. arXiv preprint arXiv:1401.7402 |