Normalized solutions to the Sobolev critical Kirchhoff-type equation with non-trapping potential

References

• Kirchhoff G. Mechanik. Leipzig: Teubner; 1883.
   Google Scholar
• Arosio A, Panizzi S. On the well-posedness of the Kirchhoff string. Trans Am Math Soc. 1996;348(1):305–330.
   Web of Science ®Google Scholar
• Carrier GF. A note on the vibrating string. Quart Appl Math. 1949;7:97–101.
   Web of Science ®Google Scholar
• Oplinger DW. Frequency response of a nonlinear stretched string. J Acoust Soc Am. 1960;32:1529–1538.
   Web of Science ®Google Scholar
• Lions J-L. On some questions in boundary value problems of mathematical physics. In: Contemporary developments in continuum mechanics and partial differential equations (Proceedings international symposium, Institute of Mathematics of the Federal University of Rio de Janeiro, Rio de Janeiro, 1977). Vol. 30, North-Holland: North-Holland Math. Stud; 1978. p. 284–346.
   Google Scholar
• Ye HY. The existence of normalized solutions for L2-critical constrained problems related to Kirchhoff equations. Z Angew Math Phys. 2015;66(4):1483–1497.
   Web of Science ®Google Scholar
• Ye HY. The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations. Math Methods Appl Sci. 2015;38(13):2663–2679.
   Web of Science ®Google Scholar
• Ye HY. The mass concentration phenomenon for L2-critical constrained problems related to Kirchhoff equations. Z Angew Math Phys. 2016;67(2):16 (Article ID: 29).
   Web of Science ®Google Scholar
• Zeng XY, Zhang YM. Existence and uniqueness of normalized solutions for the Kirchhoff equation. Appl Math Lett. 2017;74:52–59.
   Web of Science ®Google Scholar
• Luo X, Wang QF. Existence and asymptotic behavior of high energy normalized solutions for the Kirchhoff type equations in R3. Nonlinear Anal Real World Appl. 2017;33:19–32.
   Web of Science ®Google Scholar
• Li GB, Luo X, Yang T. Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent. Ann Fenn Math. 2022;47(2):895–925.
   Google Scholar
• Li QQ, Rădulescu V, Zhang J, et al. Normalized solutions of the autonomous Kirchhoff equation with Sobolev critical exponent: sub- and super-critical cases. Proc Am Math Soc. 2023;151(2):663–678.
   Web of Science ®Google Scholar
• Zhang PH, Han ZQ. Normalized ground states for Kirchhoff equations in R3 with a critical nonlinearity. J Math Phys. 2022;63(2), Paper No. 021505, 15.
   Web of Science ®Google Scholar
• Xie WH, Chen HB. Existence and multiplicity of normalized solutions for the nonlinear Kirchhoff type problems. Comput Math Appl. 2018;76(3):579–591.
   Web of Science ®Google Scholar
• Guo HL, Zhang YM, Zhou HS. Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential. Commun Pure Appl Anal. 2018;17(5):1875–1897.
   Web of Science ®Google Scholar
• Hu TX, Tang CL. Limiting behavior and local uniqueness of normalized solutions for mass critical Kirchhoff equations. Calc Var Partial Differ Equ. 2021;60(6):210 (26).
   Web of Science ®Google Scholar
• Li GB, Ye HY. On the concentration phenomenon of L2-subcritical constrained minimizers for a class of Kirchhoff equations with potentials. J Differ Equ. 2019;266(11):7101–7123.
   Web of Science ®Google Scholar
• Li YH, Hao XC, Shi JP. The existence of constrained minimizers for a class of nonlinear Kirchhoff–Schrödinger equations with doubly critical exponents in dimension four. Nonlinear Anal. 2019;186:99–112.
   Web of Science ®Google Scholar
• Jeanjean L. Existence of solutions with prescribed norm for semilinear elliptic equations. Nonlinear Anal. 1997;28(10):1633–1659.
   Web of Science ®Google Scholar
• Willem M. Minimax theorems. Boston, MA: Birkhäuser Boston, Inc.; 1996 (Progress in nonlinear differential equations and their applications; Vol. 24).
   Google Scholar
• Ding YH, Zhong XX. Normalized solution to the Schrödinger equation with potential and general nonlinear term: mass super-critical case. J Differ Equ. 2022;334:194–215.
   Web of Science ®Google Scholar
• Ghoussoub NA, Yuan C. Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents. Trans Am Math Soc. 2000;352(12):5703–5743.
   Web of Science ®Google Scholar
• Nirenberg L. On elliptic partial differential equations. Ann Scuola Norm Sup Pisa Cl Sci (3). 1959;13:115–162.
   Google Scholar
• Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 2001 (Classics in mathematics). Reprint of the 1998 edition.
   Google Scholar
• D'Aprile T, Mugnai D. Non-existence results for the coupled Klein–Gordon–Maxwell equations. Adv Nonlinear Stud. 2004;4(3):307–322.
   Web of Science ®Google Scholar
• Chang K-C. Methods in nonlinear analysis. Berlin: Springer-Verlag; 2005 (Springer monographs in mathematics).
   Google Scholar
• Ghoussoub N. Duality and perturbation methods in critical point theory. Cambridge: Cambridge University Press; 1993 (Cambridge tracts in mathematics; Vol. 107). With appendices by David Robinson.
   Google Scholar