[1] Bahri A, Coron J M. On a nonlinear elliptic equation involving the critical Sobolev exponent:The effect of the topology of the domain. Comm Pure Appl Math, 1988, 41:253-294
[2] Barrios B, Colorado E, de Pablo A, S'anchez U. On some critical problems for the fractional Laplacian. J Differential Equations, 2012, 252:6133-6162
[3] Bisci G M, Molica G, Radulescu V D, Servadei R. Variational methods for nonlocal fractional problems. Vol 162. Cambridge University Press, 2016
[4] Barrios B, Medina M, Peral I. Some remarks on the solvability of non-local elliptic problems with the Hardy potential. Commun Contemp Math, 2014, 16. DOI:10.1142/S0219199713500466
[5] Chen J. Existence of solutions for a nonlinear PDE with an inverse square potential. J Differential Equations, 2003, 195:497-519
[6] Cao D, Han P. Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J Differential Equations, 2004, 205:521-537
[7] Chi W, Kim S, Lee K. Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian. J Functional Anal,2014, 266:6531-6598
[8] Cao D, Kang D. Solutions of quasilinear elliptic problems involving a Sobolev exponent and multiple Hardy type terms. J Math Anal Appl, 2007, 333:889-903
[9] Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Comm Part Diff Equ, 2007, 32:1245-1260
[10] Cotsiolis A, Tavoularis N K. Best constants for Sobolev inequalities for higher order fractional derivatives. J Math Anal Appl, 2004, 295:225-236
[11] Cabré X, Tan J. Positive solutions for nonlinear problems involving the square root of the Laplacian. Adv Math, 2010, 224:2052-2093
[12] Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math, 2012, 136:521-573
[13] Fall M M. Semilinear elliptic equations for the fractional Laplacian with Hardy potential. Nonlinear Analysis, 2018. https://doi.org/10.1016/j.na.2018.07.008
[14] Fall M M, Felli V. Unique continuation property and local asymptotic of solutions to fractional elliptic equations. Comm Part Diff Equ, 2014, 39:354-397
[15] Ferrero A, Gazzola F. Existence of solutions for singular critical growth semilinear elliptic equations. J Differential Equations, 2001, 177:494-522
[16] Frank R L, Lieb E H, Seiringer R. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J Amer Math Soc, 2008, 21(4):925-950
[17] Filippucci R, Pucci P, Robert F. On a p-Laplace equation with multiple critical nonlinearities. J Math Pures Appl, 2009, 91:156-177
[18] Ghoussoub N, Robert F, Shakerian S, Zhao M. Mass and asymptotics associated to fractional HardySchrödinger operators in critical regimes. Comm Partial Differential Equations, 2018, 43(6):859-892
[19] Ghoussoub N, Shakerian S. Borderline variational problems involving fractional Laplacians and critical singularities. Advanced Nonlinear Studies, 2016, 15(3):93-100
[20] Herbst I. Spectral theory of the operator (p2 + m2) 1/2-Z (e2/r). Communications in Mathematical Physics, 1977, 53:285-294
[21] Passaseo D. Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains. Manuscripta Math, 1989, 65:147-166
[22] Smets D. Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans Amer Math Soc, 2005, 357:2909-2938
[23] Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm Pure Appl Math, 2007, 60(1):67-112
[24] Shakerian S. Multiple positive solutions for Nonlocal elliptic problems involving the Hardy potential and concave-convex nonlinearities. arXiv:1708.01369v1
[25] Shakerian S. Existence result for non-linearly perturbed hardy-Schrödinger problems:local and nonlocal case. arXiv:1711.08839v1
[26] Servadei R, Valdinoci E. The Brezis-Nirenberg result for the fractional Laplacian. Trans Amer Math Soc, 2015, 367:67-102
[27] Terracini S. On positive entire solutions to a class of equations with a singular coefficient and critical exponent. Adv Differential Equations,1996, 1:241-264
[28] Wang C, Yang J, Zhou J. Solutions for a nonlocal elliptic equation involving critical growth and hardy potential. preprint, 2015. arXiv:1509.07322v1
[29] Yang J. Fractional Sobolev-Hardy inequality in RN. Nonlinear Anal, 2015, 119:179-185
[30] Yang J, Yu X. Fractional Hardy-Sobolev elliptic problems. 2015. arXiv:1503.00216
[31] Zhang J, Liu X. Three solutions for a fractional elliptic problems with critical and supercritical growth. Acta Mathematica Scientia, 2016, 36B(6):1-13
[32] Zhang J, Liu X, Jiao H. Multiplicity of positive solutions for a fractional laplacian equations involving critical nonlinearity. Topol Methods Nonlinear Anal, 2019, 53(1):151-182 |