References
- Dávila J, Del Pino M, Dipierro S, Valdinoci E. Concentration phenomena for the nonlocal Schrödinger equation with dirichlet datum. Anal. PDE. 2015;8:1165–1235.
- Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys Lett A. 2000;268:298–305.
- Laskin N. Fractional Schrödinger equation. Phys Rev E. 2002;66:056108 7 pages.
- Dávila J, Del Pino M, Wei J. Concentrating standing waves for the fractional nonlinear Schrödinger equation. J Differ Equ. 2014;256:858–892.
- Fall MM, Mahmoudi F, Valdinoci E. Ground states and concentration phenomena for the fractional Schrödinger equation. Nonlinearity. 2015;28:1937–1961.
- Bartsch T, Wang Z-Q. Existence and multiplicity results for some surperlinear elliptic problems on ℝN. Comm Part Diff Eq. 1995;20:1725–1741.
- Rabinowitz PH. On a class of nonlinear Schrödinger equations. Z Angew Math Phys. 1992;43:270–291.
- Sirakov B. Existence and multiplicity of solutions of semi-linear elliptic equations in ℝN. Cal Var Partial Differ Equ. 2000;11:119–142.
- Cheng M. Bound state for the fractional Schrödinger equation with unbounded potential. J Math Phys. 2012;53:043507 8 pages.
- Secchi S. Ground state solutions for nonlinear fractional Schrödinger equations in ℝN. J Math Phys. 2013;54:031501–031501.
- Felmer P, Quaas A, Tan J. Positive solutions of nonlinear Schrödinger equation with the fractional laplacian. Proc Royal Soc Edinburgh: Sect A Math. 2012;142:1237–1262.
- Dipierro S, Palatucci G, Valdinoci E. Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian. Matematiche. 2013;68:201–216.
- Berestycki H, Lions P-L. Nonlinear scalar field equations I. Existence of a ground state. Arch Ration Mech Anal. 1983;82:313–345.
- Chang X, Wang Z-Q. Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity. Nonlinearity. 2013;26:479–494.
- do \’{O} JM, Miyagaki OH, Squassina M. Critical and subcritical fractional problems with vainshing potentials. Commun Contemp Math. 2016;18:1550063. doi:10.1142/S0219199715500637.
- Shang X, Zhang J, Yang Y. On fractional Schrödinger equation in ℝN with critical growth. J Math Phys. 2013;54. Article ID: 121502. 19 pages.
- de Souza M, Araújo YLR. On nonlinear perturbations of a periodic fractional Schrödinger equation with critical exponential growth. Math Nachr. 2016;289:610–625.
- de Souza M, Araújo YLR. Semilinear elliptic equations for the fractional Laplacian involving critical exponential growth. Math Methods Appl Sci. 2016. doi:10.1002/mma.4095.
- do \’{O} JM, Miyagaki OH, Squassina M. Nonautonomous fractional problems with exponential growth. Nonlinear Differ Equ Appl. 2015;22:1395–1410.
- Iannizzotto A, Squassina M. 1/2-laplacian problems with exponential nonlinearity. J Math Anal Appl. 2014;414:372–385.
- Servadei R, Valdinoci E. Mountain pass solution for non-local elliptic operators. J Math Anal Appl. 2012;389:887–898.
- Servadei R, Valdinoci E. Variational methods for nonlocal operators of elliptic type. Discrete Contin Dyn Syst. 2013;33:2105–2137.
- Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
- Servadei R, Valdinoci E. Weak and viscosity solutions of the fractional Laplace equation. Publ Mat. 2014;58:133–154.
- Ambrosetti A, Rabinowitz PH. Dual variational methods in critical point theory and applications. J Funct Anal. 1973;14:349–381.
- Secchi S. On fractional Schrödinger equations in ℝN without the Ambrosetti-Rabinowitz condition. Topol Methods Nonlinear Anal. 2016;47:19–41.