[1] Abdellaoui B., Mahmoudi F., An improved Hardy inequality for a nonlocal operator, Discrete Contin. Dyn. Syst., 2016, 36(3):1143-1157.
[2] Abdellaoui B., Peral I., Primo A., A remark on the fractional Hardy inequality with a remainder term, C. R. Math. Acad. Sci., Paris, 2014, 352(4):299-303.
[3] Barrios B., Medina M., Peral I., Some remarks on the solvability of non-local elliptic problems with the Hardy potential, Communications in Contemporary Mathematics, 2014, 16(4):1350046, 29 pp.
[4] Brézis H., Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Communications on Pure and Applied Mathematics, 1983, 36(4):437-477.
[5] Bucur C., Valdinoci E., Nonlocal diffusion and applications, MR3469920.
[6] Chen W. J., Fractional elliptic problems with two critical Sobolev-Hardy exponents, Electronic Journal of Differential Equations, 2018, 2018(22):1-12.
[7] Chen W. J., Deng S. B., The Nehari manifold for nonlocal elliptic operators involving concave-convex nonlinearities, Zeitschrift Für Angewandte Mathematik Und Physik, 2014, 66(4):1387-1400.
[8] Cotsiolis A., Best constants for Sobolev inequalities for higher order fractional derivatives, Journal of Mathematical Analysis and Applications, 2004, 295(1):225-236.
[9] Cotsiolis A., Tavoularis N. K., Best constants for Sobolev inequalities for higher order fractional derivatives, J Math Anal Appl, 2004, 295(1):225-236.
[10] Di N. E., Palatucci G., Valdinoci E., Hitchhiker's guide to the fractional Sobolev spaces, Bulletin Des Sciences Mathématiques, 2011, 136(5):521-573.
[11] Dipierro S., Montoro L., Peral I., et al., Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential, Calculus of Variations and Partial Differential Equations, 2016, 55(4):1-29.
[12] Fall M. M., Semilinear elliptic equations for the fractional Laplacian with Hardy potential, MR4062961.
[13] Fall M. M., Minlend I. A., Thiam E. A., The role of the mean curvature in a Sobolev-Hardy trace inequality, Nonlinear Differential Equations Application, 2014, 22(5):1-20.
[14] Felmer P., Quaas A., Tan J. G., Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian, Proceedings of the Royal Society of Edinburgh:Section A Mathematics, 2012, 142(6):1237-1262.
[15] Fiscella A., Bisci G. M., Servadei R., Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems, Bulletin Des Sciences Mathématiques, 2016, 140(1):14-35.
[16] Frank R. L., Lieb E. H., Seiringer R., Hardy-Lieb-Thirring inequalities for fractional Schrodinger operators, J. Amer. Math. Soc., 2008, 21(4):925-950.
[17] Ghoussoub N., Shakerian S., Borderline variational problems involving fractional Laplacians and critical singularities, Advanced Nonlinear Studies, 2015, 15(3):527-555.
[18] Jin L., A Global Compact Result for a Fractional Elliptic Problem with Hardy term and critical non-linearity on the whole space, arXiv:1905.02900, 2019.
[19] Jin L. Y., Fang S. M., Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N, Electronic Journal of Differential Equations, 2018, 2018(12):1-23.
[20] Palatucci G., Pisante A., Improved Sobolev embeddings, profile decomposition, and concentrationcompactness for fractional Sobolev spaces, Calculus of Variations and Partial Differential Equations, 2014, 50(3-4):799-829.
[21] Servadei R., Valdinoci E., The Brezis-Nirenberg result for the fractional Laplacian, Transactions of the American Mathematical Society, 2015, 367(1):67-102.
[22] Servadei R., Valdinoci E., Fractional Laplacian equations with critical Sobolev exponent, Revista Matemática Complutense, 2015, 28(3):655-676.
[23] Shakerian S., Multiple positive solutions for Nonlocal elliptic problems involving the Hardy potential and concave-convex nonlinearities, MR4201027.
[24] Shang X. D., Zhang J. H., Yang Y., Positive solutions of nonhomogeneous fractional Laplacian problem with critical exponent, Communications on Pure and Applied Analysis, 2014, 13(2):567-584.
[25] Silvestre L., Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 2007, 60(1):67-112.
[26] Wang C., Shang Y. Y., Existence and multiplicity of solutions for Schrödinger equation with inverse square potential and Hardy-Sobolev critical exponent, Nonlinear Analysis:Real World Applications, 2019, 46(4):525-544.
[27] Wang X. Q., Yang J. F., Singular critical elliptic problems with fractional Laplacian, Electronic Journal of Differential Equations, 2015, No. 297, 12 pp.
[28] Wang C. H., Yang J. F., Zhou J., Solutions for a nonlocal elliptic equation involving critical growth and hardy potential, arXiv:1509.07322, 2015.
[29] Yang J. F., Fractional Sobolev-Hardy inequality in R^N, Nonlinear Analysis, 2015, 119:179-185.
[30] Yang J. F., Wu F., Doubly critical problems involving fractional Laplacians in R^N, Advanced Nonlinear Studies, 2017, 17(4):677-690.
[31] Yang J. F., Yu X. J., Fractional Hardy-Sobolev elliptic problems, arXiv:1503.00216, 2015.
[32] Zhang J., Liu X. C., Jiao H. Y., Multiplicity of positive solutions for a fractional laplacian equations involving critical nonlinearity, Topol Methods Nonlinear Anal., 2019, 53(1):151-182.