References
- Li GB , Ye HY . Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in ℝ3 . J Differ Equ. 2014;257:566–600.
- Zhao LG , Zhao FK . On the existence of solutions for the Schrödinger--Poisson equations. J Math Anal Appl. 2008;346:155–169.
- Laskin N . Fractional quantum mechanics and Lévy path integrals. Phys Lett A. 2000;268:298–305.
- Laskin N . Fractional Schrödinger equation. Phys Rev. 2002;66:56–108.
- Metzler R , Klafter J . The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys Rep. 2000;339:1–77.
- Silvestre L . Regularity of the obstacle problem for a fractional power of the Laplace operator. Commun Pure Appl Math. 2007;60:67–112.
- Cont R , Tankov P . Financial modeling with jump processes. Boca Raton (FL): CRC Press; 2004.
- Chang SYA , del Mar González M . Fractional Laplacian in conformal geometry. Adv Math. 2011;226:1410–1432.
- Benci V , Fortunato D . An eigenvalue problem for the Schrödinger--Maxwell equations. Top Methods Nonlinear Anal. 1998;11:283–293.
- Benci V , Fortunato D . Solitons in Schrödinger--Maxwell equations. J Fixed Point Theory Appl. 2014;15:101–132.
- D’Aprile T , Mugnai D . Non-exstence result for the coupled Klein--Gordon--Maxwell equations. Adv Nonlinear Stu. 2004;4:307–322.
- Azzollini A , Pomponio A . Ground state solutions for the nonlinear Schrödinger--Maxwell equations. J Math Anal Appl. 2008;345:90–108.
- Ambrosetti A , Ruiz D . Multiple bound states for the Schrödinger--Poisson problem. Commun Contemp Math. 2008;10:391–404.
- Ruiz D . The Schrödinger--Poisson equation under the effect of a nonlinear local term. J Funct Anal. 2006;237:655–674.
- Davila J , del Pino M , Dipierro S , et al . Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum. Anal PDE. 2015;8:1165–1235.
- Caffarelli L , Silvestre L . An extension problem related to the fractional Laplacian. Commun Partial Differ Equ. 2007;32:1245–1260.
- Felmer P , Quaas A , Tan J . Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. Proc Roy Soc Edinburgh A. 2012;142:1237–1262.
- Dipierro S , Palatucci G , Valdinoci E . Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian. Le Matematiche. 2013;LXVIII:201–216.
- Servadei R , Valdinoci E . Mountain pass solutions for non-local elliptic operators. J Math Anal Appl. 2012;389:887–898.
- Servadei R , Valdinoci E . Variational methods for non-local operators of elliptic type. Discrete Contin Dyn. Syst. 2013;33:2105–2137.
- Ambrosio V . Ground states for superlinear fractional Schrödinger equations in ℝN . Ann Acad Sci Fenn Math. 2016;41:745–756.
- Bucur C , Valdinoci E . Nonlocal diffusion and applications. Lecture notes of the Unione Matematica Italiana. Switzerland: Springer; 2016.
- Chang XJ , Wang ZQ . Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity. Nonlinearity. 2013;26:479–494.
- Dipierro S , Medina M , Valdinoci E . Fractional elliptic problems with critical growth in the whole of ℝn . Vol. 15, Lecture Notes. Scuola Normale Superiore di Pisa (New Series). Pisa: Edizioni della Normale; 2017.
- Frank R , Lenzmann E . Uniqueness of ground states for fractional Laplacians in ℝ. Acta Math. 2013;210:261–318.
- Fall MM , Mahmoudi F , Valdinoci E . Ground states and concentration phenomena for the fractional Schrödinger equation. Nonlinearity. 2015;28:1937–1961.
- Secchi S . Ground state solutions for nonlinear fractional Schrödinger equations in ℝN . J Math Phys. 2013;54:031501.
- Shang XD , Zhang JH . Ground states for fractional Schrödinger equations with critical growth. Nonlinearity. 2014;27:187–207.
- Teng KM . Multiple solutions for a class of fractional Schrödinger equation in ℝN . Nonlinear Anal Real World Appl. 2015;21:76–86.
- Teng KM , He XM . Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent. Commun Pure Appl Anal. 2016;15:991–1008.
- Jin T , Li Y , Xiong J . On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions. J Eur Math Soc. 2014;16:1111–1171.
- Zhang J , DOÓ JM , Squassina M . Fractional Schrödinger--Poisson system with a general subcritical or critical nonlinearity. Adv Nonlinear Stud. 2016;16:15–30.
- Liu ZS , Zhang JJ . Multiplicity and concentration of positive solutions for the fractional Schrödinger-Poisson systems with critical growth. ESAIM: Control Optim Calc Var. 2017;23:1515–1542.
- Murcia EG , Siciliano G . Positive semiclassical states for a fractional Schrödinger--Poisson system. Differ Integral Equ. 2017;30:231–258.
- Teng KM , Agarwal RP . Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger--Poisson system with critical growth, arXiv:1702.05387.
- Teng KM . Existence of ground state solutions for the nonlinear fractional Schrödinger--Poisson system with critical Sobolev exponent. J Differ Equ. 2016;261:3061–3106.
- Teng KM . Corrigendum to ‘Existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system with critical Sobolev exponent’. J Differ Equ. 2017;262:3132–3138.
- Coleman S , Glaser V , Martin A . Action minima among solutions to a class of euclidean scalar field equations. Commun Math Phys. 1978;58:211–221.
- Berestycki H , Lions PL . Nonlinear scalar field equations. I. Existence of a ground state. Arch Ration Mech Anal. 1983;82:313–345.
- Struwe M . The existence of surfaces of constant mean curvature with free boundaries. Acta Math. 1988;160:19–64.
- Jeanjean L . On the existence of bounded Palais--Smale sequence and application to a Landesman-Lazer type problem set on ℝN . Proc Roy Soc Edinburgh Sect A. 1999;129:787–809.
- Di Nezza E , Palatucci G , Valdinoci E . Hitchhiker’s guide to the fractional sobolev spaces. Bull Sci Math. 2012;136:521–573.
- D’Avenia P , Squassina M . Ground states for fractional magnetic operators. ESAIM Control Optim Calc Var. 2018;24:1–24.
- Lieb EH , Loss M . Analysis. 2nd ed. Vol. 14, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2001.
- Sire Y , Valdinoci E . Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result. J Funct Anal. 2009;256:1842–1864.
- Shen ZF , Gao FS , Yang MB . Ground states for nonlinear fractional Choquard equations with general nonlinearities. Math Methods Appl Sci. 2016;39:4082–4098.
- d’Avenia P , Siciliano G , Squassina M . On fractional Choquard equations. Math Models Methods Appl Sci. 2015;25:1447–1476.
- Oton XR , Serra J . The Pohozaev identity for the fractional Laplacian. Arch Rat Mech Anal. 2014;213:587–628.
- Lions PL . The concentration-compactness principle in the calculus of variation. The locally compact case. Part I. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:109–145.
- Lions PL . The concentration-compactness principle in the calculus of variation. The locally compact case. Part II. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:223–283.