References
- Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys. Lett. A. 2000;268:298–305.
- Laskin N. Fractional quantum mechanics. Phys. Rev. E. 2000;62:3135–3145.
- Laskin N. Fractional Schrödinger equation. Phys. Rev. E. 2002;66:056108–056114.
- Tan J. The Brezis--Nirenberg type problem involving the square root of the Laplacian. Calc. Var. Partial Differ. Equ. 2011;42:21–41.
- Yu X. Liouville type theorems for integral equations and integral systems. Calc. Var. Partial Differ. Equ. 2013;46:75–95.
- Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 2007;32(7–9):1245–1260.
- Capella A, Dávila J, Dupaigne L, Sire Y. Regularity of radial extremal solutions for some non-local semilinear equations. Commun. Partial Differ. Equ. 2011;36:1353–1384.
- Felmer P, Quass A, Tan J. Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. Proc. R. Soc. Edinburgh Sect., A. 2012;142:1237–1262.
- Majda AJ, McLaughlin DW, Tabak EG. A one-dimensional model for dispersive wave turbulence. J. Nonlinear Sci. 1997;7:9–44.
- Lieb EH, Yau H-T. The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics. Commun. Math. Phys. 1987;112:147–174.
- Cabré X, Tan J. Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 2010;224:2052–2093.
- Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 2012;136:521–573.
- Ambrosetti A, Badiale M, Cingolani S. Semiclassical states of nonlinear Schrödinger equations. Arch. Ration. Mech. Anal. 1997;140:285–300.
- Cao D, Noussair ES, Yan S. Existence and uniqueness results on single-peaked solutions of a semilinear problem. Ann. Inst. H. Poincaré Anal. Non Linéaire. 1998;15:73–111.
- Cao D, Noussair ES, Yan S. Solutions with multiple peaks for nonlinear elliptic equations. Proc. R. Soc. Edinburgh Sect. A. 1999;129(2):235–264.
- Del Pino M, Felmer P. Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Var. Partial Differ. Equ. 1996;4:121–137.
- Del Pino M, Felmer P. Semi-classical states for nonlinear Schrödinger equations. J. Funct. Anal. 1997;149:245–265.
- Del Pino M, Felmer P. Multi-peak bound states of nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire. 1998;15:127–149.
- Del Pino M, Felmer P. Semi-classical states of nonlinear Schrödinger equations: a variational reduction method. Math. Ann. 2002;324:1–32.
- Dancer EN, Yan S. On the existence of multipeak solutions for nonlinear field equations on ℝN. Discret. Contin. Dyn. Syst. 2000;6:39–50.
- Kang X, Wei J. On interacting bumps of semi-classical states of nonlinear Schrödinger equations. Adv. Differ. Equ. 2000;5:899–928.
- Noussair ES, Yan S. On positive multipeak solutions of a nonlinear elliptic problem. J. London Math. Soc. 2000;62:213–227.
- Ambrosetti A, Malchiodi A, Ni WM. Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I. Commun. Math. Phys. 2003;235:427–466.
- Ambrosetti A, Malchiodi A, Ni WM. Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. II. Indiana Univ. Math. J. 2004;53:297–329.
- Dancer EN, Lam KY, Yan S. The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations. Abstr. Appl. Anal. 1998;3:293–318.
- Felmer P, Martinez S. Thick clusters for the radially symmetric nonlinear Schrödinger equation. Calc. Var. Partial Differ. Equ. 2008;31:231–261.
- Chen G, Zheng Y. Concentration phenomenon for fractional nonlinear Schrödinger equations. Commun. Pure Appl. Anal. 2014;13:2359–2376.
- Dávila J, Del Pino M, Wei J. Concentrating standing waves for fractional nonlinear Schrödinger equation. J. Differ. Equ. 2014;256:858–892.
- Dávila J, Del Pino M, Dipierro S, Valdinoci E. Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum. arXiv:1403.4435v1
- Shang X, Zhang J. Concentrating solutions of nonlinear fractional Schrödinger equation with potentials. J. Differ. Equ. 2015;258:1106–1128.
- Cao D, Peng S. Semi-classical bound states for Schrödinger equations with potentials vanishing or unbounded at infinity. Commun. Partial Differ. Equ. 2009;34:1566–1591.
- Frank R, Lenzmann E. Uniqueness and nondegeneracy of ground states for (–Δ)s Q + Q – Qα+1 = 0 in ℝ. Acta Math. 2013;210:261–318.
- Frank R, Lenzmann E, Silvestre Luis. Uniqueness of radial solutions for the fractional Laplacian. arXiv:1302.2652 2013
- Wei J, Yan S. Infinite many positive solutions for the prescribed scalar curvature problem on 𝕊N. J. Funct. Anal. 2010;258:3048–3081.