Uniqueness of non-negative solutions to an integral equation of the Choquard type

References

• Le P. Symmetry and classification of solutions to an integral equation of the Choquard type. C R Math Acad Sci Paris. 2019;357(11–12):878–888.
   Web of Science ®Google Scholar
• Le P. Liouville theorems for an integral equation of Choquard type. Commun Pure Appl Anal. 2020;19(2):771–783.
   Web of Science ®Google Scholar
• Dai W, Liu Z, Qin G. Classification of nonnegative solutions to static Schrödinger–Hartree–Maxwell type equations. SIAM J Math Anal. 2021;53(2):1379–1410.
   Web of Science ®Google Scholar
• Le P. Liouville theorem and classification of positive solutions for a fractional Choquard type equation. Nonlinear Anal. 2019;185:123–141.
   Web of Science ®Google Scholar
• Pekar S. Untersuchung über die Elektronentheorie der Kristalle. Berlin: Akademie Verlag; 1954.
   Google Scholar
• Lieb EH, Simon B. The Hartree–Fock theory for Coulomb systems. Comm Math Phys. 1977;53(3):185–194.
   Web of Science ®Google Scholar
• Moroz IM, Penrose R, Tod P. Spherically-symmetric solutions of the Schrödinger–Newton equations. Classical Quantum Gravity. 1998;15(9):2733–2742. Topology of the Universe Conference (Cleveland, OH, 1997).
   Web of Science ®Google Scholar
• Belchior P, Bueno H, Miyagaki OH, et al. Remarks about a fractional Choquard equation: ground state, regularity and polynomial decay. Nonlinear Anal. 2017;164:38–53.
   Web of Science ®Google Scholar
• d'Avenia P, Siciliano G, Squassina M. On fractional Choquard equations. Math Models Methods Appl Sci. 2015;25(8):1447–1476.
   Web of Science ®Google Scholar
• Gao F, Yang M. A strongly indefinite Choquard equation with critical exponent due to the Hardy–Littlewood–Sobolev inequality. Commun Contemp Math. 2018;20(4):1750037. 22.
   Web of Science ®Google Scholar
• Le P. On classical solutions to the Hartree equation. J Math Anal Appl. 2020;485(2):123859.
   Web of Science ®Google Scholar
• Le P. Classical solutions to a Hartree type system. Math Nachr. 2021;294(12):2355–2366.
   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(2):455–467.
   Web of Science ®Google Scholar
• Moroz V, Van Schaftingen J. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265(2):153–184.
   Web of Science ®Google Scholar
• Moroz V, Van Schaftingen J. Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent. Commun Contemp Math. 2015;17(5):1550005.
   Web of Science ®Google Scholar
• Moroz V, Van Schaftingen J. A guide to the Choquard equation. J Fixed Point Theory Appl. 2017;19(1):773–813.
   Web of Science ®Google Scholar
• Liu S. Regularity, symmetry, and uniqueness of some integral type quasilinear equations. Nonlinear Anal. 2009;71(5–6):1796–1806.
   Web of Science ®Google Scholar
• Lei Y. Liouville theorems and classification results for a nonlocal Schrödinger equation. Discrete Contin Dyn Syst. 2018;38(11):5351–5377.
   Web of Science ®Google Scholar
• Xu D, Lei Y. Classification of positive solutions for a static Schrödinger–Maxwell equation with fractional Laplacian. Appl Math Lett. 2015;43:85–89.
   Web of Science ®Google Scholar
• Dai W, Huang J, Qin Y, et al. Regularity and classification of solutions to static Hartree equations involving fractional Laplacians. Discrete Contin Dyn Syst. 2019;39(3):1389–1403.
   Web of Science ®Google Scholar
• Guo L, Hu T, Peng S, et al. Existence and uniqueness of solutions for Choquard equation involving Hardy–Littlewood–Sobolev critical exponent. Calc. Var. Partial Differ. Equ. 2019;Paper No. 58(4):128. 34.
   Web of Science ®Google Scholar
• Lei Y. On the regularity of positive solutions of a class of Choquard type equations. Math Z. 2013;273(3–4):883–905.
   Web of Science ®Google Scholar
• Chen W, Li C, Li Y. A direct method of moving planes for the fractional Laplacian. Adv Math. 2017;308:404–437.
   Web of Science ®Google Scholar
• Le P. Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order. Discrete Contin Dyn Syst. 2021;41(4):1605–1626.
   Web of Science ®Google Scholar
• Lieb EH. Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities. Ann Math (2). 1983;118(2):349–374.
   Web of Science ®Google Scholar
• Stein EM. Singular integrals and differentiability properties of functions. Princeton, NJ: Princeton University Press; 1970. (Princeton Mathematical Series; 30).
   Google Scholar
• Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math. 2006;59(3):330–343.
   Web of Science ®Google Scholar
• Kulczycki T. Properties of Green function of symmetric stable processes. Probab Math Statist. 1997;17(2, Acta Univ. Wratislav. No. 2029):339–364.
   Google Scholar
• Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm Pure Appl Math. 2007;60(1):67–112.
   Web of Science ®Google Scholar
• Chen W, D'Ambrosio L, Li Y. Some Liouville theorems for the fractional Laplacian. Nonlinear Anal. 2015;121:370–381.
   Web of Science ®Google Scholar