References
- Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys. Lett. A. 2000;268:298–305.
- Laskin N. Fractals and quantum mechanics. Chaos. 2000;10:780–790.
- Laskin N. Fractional Schrödinger equation. Phys. Rev. E. 2002;66:056108.
- Gardiner CW, Zoller P. Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Berlin: Springer; 2000.
- de Bouard A, Debussche A. A stochastic nonlinear Schrödinger equation with multiplicative noise. Comm. Math. Phys. 1999;205:161–181.
- de Bouard A, Debussche A. On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Probab. Theory Relat. Fields. 2002;123:76–96.
- de Bouard A, Debussche A. The stochastic nonlinear Schrödinger equation in H1. Stoch. Anal. Appl. 2003;21:97–126.
- de Bouard A, Debussche A. Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise. Ann. Probab. 2005;33:1078–1110.
- Debussche A, Gautier E. Small noise asymptotic of the timing jitter in soliton transmission. Ann. Appl. Probab. 2008;18:178–208.
- Gautier E. Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise. Stoch. Process. Appl. 2005;115:1904–1927.
- Gautier E. Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equations. Ann. Probab. 2008;36:896–930.
- Rasmussen KO, Gaididei YB, Bang O, Chrisiansen PL. The influence of noise on critical collapse in the nonlinear Schrödinger equation. Phys. Lett. A. 1995;204:121–127.
- Kwaśnicki M. Eigenvalues of fractional Laplace operator in the interval. J. Funct. Anal. 2012;262:2379–2402.
- Du Q, Gunzburger M, Lehoucq RB, et al. Analysis and approximation of nonlocal diffusion problems with volume constraints. SIAM Rev. 2012;54:667–696.
- Guo B, Huo Z. Global well-posedness for the fractional nonlinear Schrödinger equation. Comm. Partial Differ. Equ. 2011;36:247–255.
- Cho Y, Ozawa T. On the semirelativistic Hartree-type equation. SIAM J. Math. Anal. 2006;38:1060–1074.
- Frank R, Lenzmann E. Uniqueness of non-linear ground states for fractional Laplacians in ℝ. Acta Math. 2013;210:261–318.
- Fröhlich J, Jonsson B, Lenzmann E. Boson stars as solitary waves. Comm. Math. Phys. 2007;274:1–30.
- Fröhlich J, Lenzmann E. Blow up for nonlinear wave equations describing boson stars. Comm. Pure Appl. Math. 2007;60:1691–1705.
- Guo B, Huang D. Existence and stability of standing waves for nonlinear fractional Schrödinger equations. J. Math. Phys. 2012;53:083702.
- Ionescu A, Pusateri F. Nonlinear fractional Schrödinger equations in one dimension. J. Funct. Anal. 2014;266:139–176.
- Krieger J, Lenzmann E, Raphaël P. Nondispersive solutions to the L\textsuperscript{2}-critical half-wave equation. Arch. Rat. Mech. Anal. 2013;209:61–129.
- Lenzmann E. Well-posedness for semi-relativistic Hartree equations of critical type. Math. Phys. Anal. Geom. 2007;10:43–64.
- Lenzmann E, Lewin M. On singularity formation for the L\textsuperscript{2}-critical Boson star equation. Nonlinearity. 2011;24:3515–3540.
- Lions JL. Quelques methodes de resolution des problems aux limites non lineaires [Some methods of resolving problem with nonlinear limits]. Paris: Dunod; 1969.
- Michelangeli A, Schlein B. Dynamical collapse of boson stars. Comm. Math. Phys. 2012;311:645–687.
- Cho Y, Hwang G, Kwon S, et al. Well-posedness and ill-posedness for the cubic fractional Schrödinger equations. 2013. arXiv:1311.0082v3 [math.AP].
- Tsutsumi Y. L\textsuperscript{2}-solutions for nonlinear Schrödinger equations and nonlinear groups. Funkcialaj Ekvacioj. 1987;30:115–125.
- Wu E, Tang Y. Blow-up solutions to the Cauchy problem of a fractional reaction--diffusion system. J. Inequal. Appl. 2015.
- Cazenave T. Semilinear Schr\"{o}inger equations. Courant lecture notes in mathematics. Vol. 10. Providence (RI): NYU, CIMS, AMS; 2003.
- Du Q, Gunzburger M, Lehoucq RB, et al. A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math. Models Methods Appl. Sci. 2013;23:493–540.
- Nezza ED, Palatucci G, Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 2012;136:521–573.
- Flandoli F, Gatarek D. Martingale and stationary solutions for stochastic Navier--Stokes equations. Probab. Theory Relat. Fields. 1995;102:367–391.
- Temam R. Navier--Stokes equations and nonlinear functional analysis. Philadelphia: SIAM; 1983.
- Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Vol. 44, Encyclopedia of mathematics and its applications. Cambridge: Cambridge University Press; 1992.
- Billingsley P. Convergence of probability measures. 2nd ed., New York (NY): Wiley; 1999.
- Ikeda N, Watanabe S. Stochastic differential equations and diffusion processes. Amsterdam: North-Holland; 1981.
- Billingsley P. Probability and measure. 2nd ed., Wiley series in probability and mathematical statistics. Probability and mathematical statistics. New York (NY): Wiley; 1986. MR 830424 (87f:60001).
- Jakubowski A. The almost sure Skorohod representation for subsequences in nonmetric spaces. Teor. Veroyatnost. i Primenen. 1997;42:209–216; Theory Probab. Appl. 1998;42:167–174.
- Remmert R. Classical topics in complex function theory. New York (NY): Springer; 1998.
- Porter MB. Concerning series of analytic functions. Ann. Math. 2nd Ser. 6:190–192; 1905.