Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 15
90
Views
0
CrossRef citations to date
0
Altmetric
Articles

Radial and asymptotically constant solutions for nonautonomous elliptic equations

, &
Pages 3132-3144 | Received 29 May 2019, Accepted 28 Dec 2019, Published online: 14 Jan 2020

References

  • Berestycki H, Lions PL. Existence d'ondes solitaires dans des problèmes non-linéaires du type Klein–Gordon (French). C R Acad Sci Paris Sér A-B. 1978;287(7):A503–A506.
  • Berestycki H, Lions PL. Existence of a ground state in nonlinear equations of the Klein–Gordon type. Variational inequalities and complementarity problems, pp. 35–51, Chichester: Wiley; 1980. (Proc. Int. School, Erice; 1978).
  • Strauss WA. Existence of solitary waves in higher dimensions. Comm Math Phys. 1977;55(2):149–162.
  • Berestycki H, Nirenberg L. On the method of moving planes and the sliding method. Bol Soc Bras Mat. 1991;22:1–37.
  • Gidas B, Ni W, Nirenberg L. Symmetry and related properties via the maximum principle. Comm Math Phys. 1979;68:209–243.
  • Berger MS. On the existence and structure of stationary states for a nonlinear Klein–Gordon equation. J Funct Anal. 1972;9:249–261.
  • Coffman CV. Uniqueness of the ground state solution for Δu−u+u3=0 and a variational characterization of other solutions. Arch Ration Mech Anal. 1972;46:81–95.
  • Ibrahim H. Radial solutions of semilinear elliptic equations with prescribed asymptotic behavior, preprint.
  • Nehari Z. On a nonlinear differential equation arising in nuclear physics. Proc Roy Irish Acad Sect A. 1963:62;117–135.
  • Ryder GH. Boundary value problems for a class of nonlinear differential equations. Pacific J Math. 1967;22:477–503.
  • Ibrahim H, Nasreddine E. Existence of semilinear elliptic equations with prescribed limiting behaviour. Math Methods Appl Sci. 2016;39(14):4129–4138.
  • Ibrahim H, Nasreddine E. On the existence of nonautonomous ODE with application to semilinear elliptic equations. Med J Math. 2018;15(2):15:64.
  • Pohozaev SI. Eigenfunctions of the equations Δu+λf(u)=0. Sov Math Dokl. 1965;5:1408–1411.
  • Bonheure D, Grossi M, Noris B et al., Multi-layer radial solutions for a supercritical Neumann problem. J. Differ Equ. 2016;261(1):455–504.
  • Bonheure D, Grumiau C, Troestler C. Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions. Nonlinear Anal. 2016;147:236–273.
  • Boscaggin A, Colasuonno F, Noris B. Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions. ESAIM Control Optim Calc Var. 2018;24(4):1625–1644.

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.