Geodesic
Ground states for fractional Choquard equations with doubly critical exponents and magnetic fields
Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 43-53.

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In this paper, we investigate the ground states for the fractional Choquard equations with doubly critical exponents and magnetic fields. We prove that the equation has a ground state solution by using the Nehari method and the Pokhozhaev identity.
Keywords: magnetic fields, doubly critical exponents, Nehari method, Pokhozhaev identity.
Mots-clés : fractional Choquard equation 
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Zhenyu Guo; Lujuan Zhao. Ground states for fractional Choquard equations with doubly critical exponents and magnetic fields. Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/IM2_2024_88_1_a2/

[1] P. d'Avenia and M. Squassina, “Ground states for fractional magnetic operators”, ESAIM Control Optim. Calc. Var., 24:1 (2018), 1–24 | DOI | MR | Zbl

[2] T. Ichinose and H. Tamura, “Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field”, Comm. Math. Phys., 105:2 (1986), 239–257 | DOI | MR | Zbl

[3] Li Ma and Lin Zhao, “Classification of positive solitary solutions of the nonlinear Choquard equation”, Arch. Ration. Mech. Anal., 195:2 (2010), 455–467 | DOI | MR | Zbl

[4] V. Moroz and J. Van Schaftingen, “Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics”, J. Funct. Anal., 265:2 (2013), 153–184 | DOI | MR | Zbl

[5] P. d'Avenia, G. Siciliano, and M. Squassina, “On fractional Choquard equations”, Math. Models Methods Appl. Sci., 25:8 (2015), 1447–1476 | DOI | MR | Zbl

[6] Jinmyoung Seok, “Nonlinear Choquard equations: doubly critical case”, Appl. Math. Lett., 76 (2018), 148–156 | DOI | MR | Zbl

[7] Yu Su, Li Wang, Haibo Chen, and Senli Liu, “Multiplicity and concentration results for fractional Choquard equations: doubly critical case”, Nonlinear Anal., 198 (2020), 111872 | DOI | MR | Zbl

[8] Chun-Yu Lei and Binlin Zhang, “Ground state solutions for nonlinear Choquard equations with doubly critical exponents”, Appl. Math. Lett., 125 (2022), 107715 | DOI | MR | Zbl

[9] E. H. Lieb and M. P. Loss, Analysis, Grad. Stud. Math., 14, 2nd ed., Amer. Math. Soc., Providence, RI, 2001 | DOI | MR | Zbl

[10] Zifei Shen, Fashun Gao, and Minbo Yang, Groundstates for nonlinear fractional Choquard equations with general nonlinearities, 2014, arXiv: 1412.3184

[11] A. Szulkin and T. Weth, “The method of Nehari manifold”, Handbook of nonconvex analysis and applications, Int. Press, Somerville, MA, 2010, 597–632 | MR | Zbl

[12] M. Willem, Minimax theorems, Progr. Nonlinear Differential Equations Appl., 24, Birkhäuser Boston, Inc., Boston, MA, 1996 | DOI | MR | Zbl