Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 7
165
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Schrödinger–Kirchhof-type problems involving the fractional p-Laplacian with exponential growth

, &
Pages 1942-1974 | Received 09 Aug 2021, Accepted 19 Nov 2021, Published online: 06 Dec 2021

References

  • Trudinger NS. On imbeddings into Orlicz spaces and some applications. J Math Mech. 1967;17:473–483.
  • Moser J. A sharp form of an inequality by N. Trudinger. Indiana Univ Math J. 1971;20:1077–1092.
  • Martinazzi L. Fractional Adams–Moser–Trudinger type inequalities. Nonlinear Anal. 2015;127:263–278.
  • Parini E, Ruf B. On the Moser–Trudinger inequality in fractional Sobolev–Slobodeckij spaces. Rend Lincei-Mat Appl. 2018;29:315–319.
  • Iula S. A note on the Moser-Trudinger inequality in Sobolev–Slobodeckij spaces in dimension one. Rend Lincei-Mat Appl. 2017;28:871–884.
  • Mingqi X, Rădulescu VD, Zhang B. Fractional Kirchhoff problems with critical Trudinger–Moser nonlinearity. Calc Var Partial Differ Equ. 2019;58:57.
  • Zhang C. Trudinger–Moser inequalities in fractional Sobolev–Slobodeckij spaces and multiplicity of weak solutions to the fractional-Laplacian equation. Adv Nonlinear Stud. 2019;19:197–217.
  • Thin NV. Singular Trudinger–Moser inequality and fractional p-Laplace equations in RN. Nonlinear Anal. 2020;196:111756.
  • Miyagaki OH, Pucci P. Nonlocal Kirchhoff problems with Trudinger–Moser critical nonlinearities. Nonlinear Differ Equ Appl. 2019;26(4):27.
  • Xiang M, Zhang B, Repovš D. Existence and multiplicity of solutions for fractional Schrödinger–Kirchhoff equations with Trudinger–Moser nonlinearity. Nonlinear Anal. 2019;186:74–98.
  • Molica Bisci G, Rădulescu V, Servadei R. Variational methods for nonlocal fractional problems. Cambridge: Cambridge University Press; 2016.
  • Chipot M, Rodrigues JF. On a class of nonlocal nonlinear elliptic problems. ESAIM: Math Model Numer Anal. 1992;26:447–467.
  • Lions JL. On some questions in boundary value problems of mathematical physics. In Contemporary developments in continum mechanics and partial differential equations. Vol. 30. Proceedings of the International Symposium (Institute of Mathematics of the Federal University of Rio de Janeiro, Rio de Janeiro, North-Holland Mathematics Studies); 1977. p. 284–346.
  • Mingqi X, Rădulescu VD, Zhang B. Nonlocal Kirchhoff problems with singular exponential nonlinearity. Appl Math Opt. doi:10.1007/s00245-020-09666-3
  • Almgren FJ, Lieb EH. Symmetric decreasing rearrangement is sometimes continuous. J Am Math Soc. 1989;2:683–773.
  • Pucci P, Xiang M, Zhang B. Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in RN. Calc Var Partial Differ Equ. 2015;54:2785–2806.
  • Binlin Z, Rădulescu V, Wang L. Existence results for Kirchhoff-type superlinear problems involving the fractional Laplacian. Proc R Soc Edinb A. 2019;149:1061–1081.
  • Jeanjean L. On the existence of bounded Palais-Smale sequences and application to a Landesman–Lazer type problem set on RN. Proc R Soc Edinb A. 1999;129:787–809.
  • Binlin Z, Molica Bisci G, Servadei R. Superlinear nonlocal fractional problems with infinitely many solutions. Nonlinearity. 2015;28:2247–2264.
  • Binlin Z, Molica Bisci G, Xiang M. Multiplicity results for nonlocal fractional p-Kirchhoff equations via Morse theory. Topol. Methods Nonlinear Anal. 2017;49:445–461.
  • Liu S. On ground states of superlinear p-Laplacian equations in RN. J Math Anal Appl. 2010;361:48–58.
  • Caponi M, Pucci P. Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations. Ann Mat Pura Appl. 2016;195:2099–2129.
  • Nezza ED, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
  • Lia Q, Yang Z. Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in RN. Complex Var Elliptic Equ. 2016;61:969–983.
  • Struwe M. Variational methods, applications to nonlinear partial differential equations and Hamiltonian systems. Berlin: Springer; 1990. (Ergebnisse der Mathematik und ihrer Grenzgebiete).
  • Willem M. Minimax theorems. Basel: Birkhäuser; 1996.
  • Cerami G. An existence criterion for the critical points on unbounded manifolds (in Italian). Ist Lombardo Accad Sci Lett Rend Sez A. 1978;112:332–336.
  • Cerami G. On the existence of eigenvalues for a nonlinear boundary value problem (in Italian). Ann Mat Pura Appl. 1980;124:161–179.
  • Rabinowitz PH. Minimax methods in critical point theory with applications to differential equations. Providence (RI): American Mathematical Society; 1986. (CBMS regional conference series in mathematics; vol. 65).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.