F.J. Almgren and E.H. Lieb, Symmetric decreasing rearrangement is sometimes continuous, J. Amer. Math. Soc. 2 (1989), 683–773.

D. Applebaum, Lévy processes-from probability to finance and quantum groups, Notices Amer. Math. Soc. 51 (2004), 1336–1347.

G. Autuori, A. Fiscella and P. Pucci, Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity, Nonlinear Anal. 125 (2015), 699–714.

T. Bartsch, L. Jeanjean and N. Soave, Normalized solutions for a system of coupled cubic Schrödinger equations on R3 , J. Math. Pures Appl. 106 (2016), 583–614.

T. Bartsch and N. Soave, Multiple normalized solutions for a competing system of Schrödinger equations, Calc. Var. Partial Differential Equations 58 (2019), 22.

H. Berestycki and P.L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82 (1983), 347–376.

L. Caffarelli, Non-local diffusions, drifts and games, Nonlinear Partial Differential Equations, Abel Symp., vol. 7, Springer, Berlin, Heidelberg, 2012, pp. 37–52.

X. Cao, J. Xu, and J. Wang, The existence of solutions with prescribed L2 -norm for Kirchhoff type system, J. Math. Phys. 58 (2017), 041502.

T. Cazenave and P.L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982), 549–561.

J. Chang and Z. Liu, Ground states of nonlinear Schrödinger systems, Proc. Amer. Math. Soc. 138 (2010), 687–693.

X. Chang and Z.-Q. Wang, Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity, Nonlinearity 26 (2013), 479–494.

G. Che and H. Chen, Existence and asymptotic behavior of positive ground state solutions for coupled nonlinear fractional Kirchhoff-type systems, Comput. Math. Appl. 77 (2019), 173–188.

M. Chipot and B. Lovat, Some remarks on nonlocal elliptic and parabolic problems, Nonlinear Anal. 30 (1997), 4619–4627.

E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), 521–573.

M. Du, L. Tian, J. Wang and F. Zhang, Existence of normalized solutions for nonlinear fractional Schrödinger equations with trapping potentials, Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 617–653.

A. Fiscella and E. Valdinoci, A critical Kirchhoff type problem involving a nonlocal operator, Nonlinear Anal. 94 (2014), 156–170.

Z. Feng and Y. Su, Lions-type theorem of the fractional Laplacian and applications, Dyn. Partial Differ. Equ. 18 (2021), 211–230.

R. Frank, E. Lenzmann and L. Silvestre, Uniqueness of radial solutions for the fractional Laplacian, Comm. Pure Appl. Math. 69 (2016), 1671–1726.

N. Ghoussoub, Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Mathematics, vol. 107, Cambridge University Press, Cambridge, 1993.

T. Gou and L. Jeanjean, Existence and orbital stability of standing waves for nonlinear Schrödinger systems, Nonlinear Anal. 144 (2016), 10–22.

T. Gou and L. Jeanjean, Multiple positive normalized solutions for nonlinear Schrödinger systems, Nonlinearity 31 (2018), 2319–2345.

Z. Guo, S. Luo, and W. Zou, On critical systems involving fractional Laplacian, J. Math. Anal. Appl. 446 (2017), 681–706.

Y. Guo, X. Zeng, and H. Zhou, Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions, Discrete Contin. Dyn. Syst. 37 (2017), 3749–3786.

X. Huang and Y. Zhang, Existence and uniqueness of minimizers for constrained problems related to fractional Kirchhoff equation, Math. Methods Appl. Sci. 43 (2020), 8763–8775.

N. Ikoma, Compactness of minimizing sequences in nonlinear Schrödinger systems under multiconstraint conditions, Adv. Nonlinear Stud. 14 (2014), 115–136.

L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. 28 (1997), 1633–1659.

G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883.

G. Li, X. Luo and T. Yang, Normalized solutions to a class of Kirchhoff equations with sobolev critical exponent, preprint, arXiv: 2013.08106.

C. Li, Z. Wu, and H. Xu, Maximum principles and Bôcher type theorems, Proc. Natl. Acad. Sci. USA 115 (2018), 6976–6979.

G. Li and H. Ye, On the concentration phenomenon of L2 -subcritical constrained minimizers for a class of Kirchhoff equations with potentials, J. Differential Equations 266 (2019), 7101–7123.

P.L. Lions, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315–334.

P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I , Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 109–145.

P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 223–283.

Z. Liu, M. Squassina and J. Zhang, Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension, NoDEA Nonlinear Differential Equations Appl. 24 (2017), 50.

Z. Liu and Z.-Q. Wang, Multiple bound states of nonlinear Schrödinger systems, Comm. Math. Phys. 282 (2008), 721–731.

H. Luo and Z. Zhang, Normalized solutions to the fractional Schrödinger equations with combined nonlinearities, Calc. Var. Partial Differential Equations 59 (2020), 143.

D. Lü and S. Peng, Existence and asymptotic behavior of vector solutions for coupled nonlinear kirchhoff-type systems, J. Differential Equations 263 (2017), 8947–8978.

X. Ros-Oton and J. Serra, The Dirichlet problem for the fractional Laplacian: regularity up to the boundary, J. Math. Pures Appl. 101 (2014), 275–302.

M. Shibata, Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term, Manuscripta Math. 143 (2014), 221–237.

N. Soave, Normalized ground states for the NLS equation with combined nonlinearities, J. Differential Equations 269 (2020), 6941–6987.

N. Soave, Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case, J. Funct. Anal. 279 (2020), 108610.

Y. Su and H. Chen,, Fractional Kirchhoff-type equation with Hardy–Littlewood–Sobolev critical exponent, Comput. Math. Appl. 78 (2019), 2063–2082.

J. Sun and T.-F. Wu, Ground state solutions for an indefinite Kirchhoff type problem with steep potential well, J. Differential Equations 256 (2014), 1771–1792.

J. Sun, Y. Cheng, T.-F. Wu and Z. Feng, Positive solutions of a superlinear Kirchhoff type equation in RN (N ≥ 4), Commun. Nonlinear Sci. Numer. Simul. 71 (2019), 141–160.

K. Teng, Ground state solutions for the non-linear fractional Schrödinger-Poisson system, Appl. Anal. 98 (2019), 1959–1996.

M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983), 567–576.

M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, vol. 24, Birkhäuser Boston, Inc., Boston, MA, 1996.

W. Xie and H. Chen, Existence and multiplicity of normalized solutions for the nonlinear Kirchhoff type problems, Comput. Math. Appl. 76 (2018), 579–591.

Z. Yang, Normalized ground state solutions for Kirchhoff type systems, J. Math. Phys. 62 (2021), 031504.

H. Ye, The mass concentration phenomenon for L2 -critical constrained problems related to Kirchhoff equations, Z. Angew. Math. Phys. 67 (2016), 29.