Classification of positive solutions to the critical fractional Choquard equation in

References

• Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys Lett A. 2000;268:29–305. doi: 10.1016/S0375-9601(00)00201-2
   Web of Science ®Google Scholar
• Laskin N. Fractional Schrödinger equation. Phys Rev E. 2002;66:31–35. doi: 10.1103/PhysRevE.66.056108
   Web of Science ®Google Scholar
• Caffarelli L, Roquejoffre J, Sire Y. Variational problems with free boundaries for the fractional Laplacian. J Eur Math Soc. 2010;12:1151–1179. doi: 10.4171/JEMS/226
   Web of Science ®Google Scholar
• Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Commun Partial Differ Equ. 2007;32:1245–1260. doi: 10.1080/03605300600987306
   Web of Science ®Google Scholar
• Felmer P, Quaas A, Tan J. Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian. Proc Roy Soc Edinburgh Sect A. 2012;142:1237–1262. doi: 10.1017/S0308210511000746
   Google Scholar
• Gao F, Yang M. On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation. Sci China Math. 2018;61(7):1219–1242. doi: 10.1007/s11425-016-9067-5
   Web of Science ®Google Scholar
• Luo H. Ground state solutions of Pohožaev type and Nehari type for a class of nonlinear Choquard equations. J Math Anal Appl. 2018;467(2):842–862. doi: 10.1016/j.jmaa.2018.07.055
   Web of Science ®Google Scholar
• Ma L, Zhao L. Classification of positive solitary solutions of the nonlinear Choquard equation. Arch Ration Mech Anal. 2010;195:455–467. doi: 10.1007/s00205-008-0208-3
   Web of Science ®Google Scholar
• Moroz IM, Penrose R, Tod P. Spherically-symmetric solutions of the Schrödinger-Newton equations. Class Quantum Gravity. 1998;15:2733–2742. doi: 10.1088/0264-9381/15/9/019
   Web of Science ®Google Scholar
• Moroz V, Schaftingen JV. A guide to the Choquard equation. J Fixed Point Theory Appl. 2017;19(1):773–813. doi: 10.1007/s11784-016-0373-1
   Web of Science ®Google Scholar
• D'Avenia P, Siciliano G, Squassina M. On fractional Choquard equations. Math Models Methods Appl Sci. 2015;25:1447–1476. doi: 10.1142/S0218202515500384
   Web of Science ®Google Scholar
• Lieb EH. Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud Appl Math. 1976/77;57:93–105. doi: 10.1002/sapm197757293
   Web of Science ®Google Scholar
• Penrose R. On gravity's role in quantum state reduction. Gen Relativ Gravitation. 1996;28:581–600. doi: 10.1007/BF02105068
   Web of Science ®Google Scholar
• Landkof NS. Foundations of modern potential theory. New York (NY): Springer; 1972.
   Google Scholar
• Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math. 2006;59:330–343. doi: 10.1002/cpa.20116
   Web of Science ®Google Scholar
• Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573. doi: 10.1016/j.bulsci.2011.12.004
   Web of Science ®Google Scholar
• Hardy GH, Littlewood J, Polya G. Inequalities. Cambridge: Cambridge University Press; 1952.
   Google Scholar
• Riesz M. L'intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math. 1949;81:1–223. doi: 10.1007/BF02395016
   Web of Science ®Google Scholar
• Perera K, Squassina M, Yang Y. Bifurcation and multiplicity results for critical fractional p-Laplacian problems. Math Nachr. 2016;289(2–3):332–342. doi: 10.1002/mana.201400259
   Web of Science ®Google Scholar
• Lions P-L. The concentration-compactness principle in the calculus of variations, The limit case, Part 1. Rev Math Iberoam. 1985;1:145–201. doi: 10.4171/RMI/6
   Google Scholar
• Lions P-L. The concentration-compactness principle in the calculus of variations, The limit case, Part 2. Rev Math Iberoam. 1985;1:45–121. doi: 10.4171/RMI/12
   Google Scholar
• Ambrosio V. Fractional p&q Laplacian problems in RN with critical growth. arXiv preprint arXiv:1801.10449. 2018.
   Google Scholar
• Ambrosio V, Isernia T. Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional p-Laplacian. Discrete Contin Dyn Syst. 2018;38(11):5835–5881. doi: 10.3934/dcds.2018254
   Web of Science ®Google Scholar
• Zhang X, Zhang B, Repovs D. Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials. Nonlinear Anal. 2016;142:48–68. doi: 10.1016/j.na.2016.04.012
   Web of Science ®Google Scholar
• Brézis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Am Math Soc. 1983;88:486–490. doi: 10.2307/2044999
   Web of Science ®Google Scholar
• Liu S. Regularity, symmetry, and uniqueness of some integral type quasilinear equations. Nonlinear Anal. 2009;71:1796–1806. doi: 10.1016/j.na.2009.01.014
   Web of Science ®Google Scholar
• Ma C, Chen W, Li C. Regularity of solutions for an integral system of Wolff type. Adv Math. 2011;226:2676–2699. doi: 10.1016/j.aim.2010.07.020
   Web of Science ®Google Scholar
• Chen W, Jin C, Li C. Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations. Discrete Contin Dyn Syst. 2005;Supplement:164–172.
   Google Scholar
• Seok J. Limit profiles and uniqueness of ground states to the nonlinear Choquard equations. Adv Nonlinear Anal. 2019;8(1):1083–1098. doi: 10.1515/anona-2017-0182
   Web of Science ®Google Scholar
• Ambrosetti A, Azorero JG, Peral I. Perturbation of Δu+u(N+2)/(N−2)=0, the scalar curvature problem in RN, and related topics. J Funct Anal. 1999;165(1):117–149. doi: 10.1006/jfan.1999.3390
   Web of Science ®Google Scholar