References
- Moroz V, Schaftingen JV. A guide to the Choquard equation. J Fixed Point Theory Appl. 2017;19:773–813. doi: 10.1007/s11784-016-0373-1
- Pekar S. Untersuchung ber die elektronentheorie der Kristalle. Berlin: Akademie Verlag; 1954.
- Lieb EH. Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud Appl Math. 1977;57:93–105. doi: 10.1002/sapm.v57.2
- Gross EP. Physics of many-particle systems: methods and problems. Vol. I. New York: Gordon Breach; 1996.
- Penrose R. On gravity's role in quantum state reduction. Gen Relativ Gravitat. 1996;28:581–600. doi: 10.1007/BF02105068
- Moroz V, Schaftingen JV. Groundstates of nonlinear Choquard equations:existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153–184. doi: 10.1016/j.jfa.2013.04.007
- Lieb EH, Loss M. Analysis. Providence: American Mathematical Society; 2001. (Graduate Studies in Mathematics).
- Alves CO, Figueiredo GM, Yang M. Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity. Adv Nonlinear Anal. 2016;5(4):331–345. doi: 10.1515/anona-2015-0123
- Alves CO, Figueiredo GM, Molle R. Multiple positive bound state solutions for a critical Choquard equation. Discrete Contin Dyn Syst. 2021;41(10):4887–4919. doi: 10.3934/dcds.2021061
- Carvalho MLM, Silva ED, Goulart C. Choquard equations via nonlinear Rayleigh quotient for concave–convex nonlinearities. Commun Pure Appl Anal. 2021;20(10):3445–3479. doi: 10.3934/cpaa.2021113
- Cingolani S, Gallo M, Tanaka K. Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities. Calc Var Partial Differ Equ. 2022;61:68. doi: 10.1007/s00526-021-02182-4
- Li X, Liu X, Ma S. Infinitely many bound states for Choquard equations with local nonlinearities. Nonlinear Anal. 2019;189:111583. doi: 10.1016/j.na.2019.111583
- Liu Z, Moroz V. Limit profiles for singularly perturbed Choquard equations with local repulsion. Cal Var Partial Differ Equ. 2022;61(4):1–59.
- 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
- Zhang J, Wu QF, Qin DD. Semiclassical solutions for Choquard equations with Berestycki–Lions type conditions. Nonlinear Anal. 2019;188:22–49. doi: 10.1016/j.na.2019.05.016
- Alves CO, Cassani D, Tarsi C, et al. Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2. J Differ Equ. 2016;261:1933–1972. doi: 10.1016/j.jde.2016.04.021
- Alves CO, Nóbrega AB, Yang M. Multi-bump solutions for Choquard equation with deepening potential well. Calc Var Partial Differ Equ. 2016;55:48. doi: 10.1007/s00526-016-0984-9
- Bartsch T, Weth T, Willem M. Partial symmetry of least energy nodal solutions to some variational problems. J Anal Math. 2005;96:1–18. doi: 10.1007/BF02787822
- Chen S, Tang X. Ground state solutions for general Choquard equations with a variable potential and a local nonlinearity. Rev R Acad Cienc Exactas Fis Nat Ser A Mat RACSAM. 2020;114.
- Schaftingen JV, Willem M. Symmetry of solutions of semilinear elliptic problems. J Eur Math Soc (JEMS). 2008;10(2):439–456. doi: 10.4171/jems
- Silva ED, Carvalho MLM, Silva ML, et al. Superlinear fractional elliptic problems via the nonlinear Rayleigh quotient with two parameters. Math Nachr. 2024;273(3):1062–1091.doi: 10.1002/mana.202100599
- Moroz V, Schaftingen JV. Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent. Commun Contemp Math. 2015;17:1550005. doi: 10.1142/S0219199715500054
- Moroz V, Schaftingen JV. Existence of groundstates for a class of nonlinear Choquard equations. Trans Am Math Soc. 2015;367:6557–6579. doi: 10.1090/tran/2015-367-09
- Berestycki H, Lions P-L. Nonlinear scalar field equations I: existence of a ground state. Arch Ration Mech Anal. 1983;82:313–345. doi: 10.1007/BF00250555
- Brown KJ, Wu T-F. A fibering map approach to a semilinear elliptic boundary value problem. Electron J Differ Equ. 2007;69:1–9.
- Brown KJ, Wu TF. A fibering map approach to a potential operator equation and its applications. Differ Integr Equ. 2009;22:1097–1114. doi: 10.57262/die/1356019406
- Huang Y, Wu T-F, Wu Y. Multiple positive solutions for a class of concave–convex elliptic problems in RN involving sign-changing weight, II. Commun Contemp Math. 2015;17:1450045. doi: 10.1142/S021919971450045X
- Il'yasov Y. On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient. Topol Methods Nonlinear Anal. 2017;49(2):683–714.
- Il'yasov Y. On nonlocal existence results for elliptic equations with convex-concave nonlinearities. Nonlinear Anal. 2005;61(1–2):211–236. doi: 10.1016/j.na.2004.10.022
- Tarantello G. On nonhomogeneous elliptic equations involving critical Sobolev exponent. Ann Inst Henri Poincaré Anal Nonlinear. 1992;9(3):281–304. doi: 10.4171/aihpc
- Wu T-F. Multiple positive solutions for a class of concave–convex elliptic problems in RN involving sign-changing weight. J Funct Anal. 2010;258:99–131. doi: 10.1016/j.jfa.2009.08.005
- Cheng Y-H, Wu T-F. Multiplicity and concentration of positive solutions for semilinear elliptic equations with steep potentia. Commun Pure Appl Anal. 2016;15:1534–0392. doi: 10.3934/cpaa
- Ding Y, Gao F, Yang M. Semi classical states for Choquard type equations with critical growth: critical frequency case. Nonlinearity. 2020;33:6695–6728. doi: 10.1088/1361-6544/aba88d
- Gao F, Silva E, Yang M, et al. Existence of solutions for critical Choquard equations via the concentration compactness method. Proc R Soc Edinburgh Sec A Math. 2020;150:921–954. doi: 10.1017/prm.2018.131
- Gao F, Moroz V, Yang M, et al. Construction of infinitely many solutions for a critical Choquard equation via local Pohozaev identities. Calc Var Partial Differ Equ. 2022;61:222. doi: 10.1007/s00526-022-02340-2
- Lions P. The Choquard equation and related questions. Nonlinear Anal. 1980;4:1063–1072. doi: 10.1016/0362-546X(80)90016-4
- Zhang H, Zhang F. Multiplicity and concentration of solutions for Choquard equations with critical growth. J Math Anal Appl. 2020;481:123457. doi: 10.1016/j.jmaa.2019.123457
- Bartsch T, Wang ZQ. Existence and multiplicity results for some superlinear elliptic problems on RN. Commun Partial Differ Equ. 1995;20:1725–1741. doi: 10.1080/03605309508821149
- Nehari Z. On a class of nonlinear second-order differential equations. Trans Am Math Soc. 1960;95:101–123. doi: 10.1090/tran/1960-095-01
- Nehari Z. Characteristic values associated with a class of non-linear second-order differential equations. Acta Math. 1961;105:141–175. doi: 10.1007/BF02559588
- Il'yasov Y, Silva K. On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method. Proc Am Math Soc. 2018;146(7):2925–2935. doi: 10.1090/proc/2018-146-07
- Rabinowitz PH. Minimax methods in critical point theory with applications to differential equations. In: CBMS Regional Conference Series in Mathematics. Vol. 65, Published for the Conference Board of the Mathematical Sciences, Washington, DC. Providence, RI: American Mathematical Society; 1986.
- Silva K. On an abstract bifurcation result concerning homogeneous potential operators with applications to PDEs. J Differ Equ. 2020;269:7643–7675. doi: 10.1016/j.jde.2020.06.001
- Seok J. Nonlinear Choquard equations involving a critical local term. Appl Math Lett. 2017;63:77–87. doi: 10.1016/j.aml.2016.07.027
- Drábek P, Milota J. Methods of nonlinear analysis: applications to differential equations.2nd ed. Basler Lehrbücher: Birkhäuser Advanced Texts; 2013.