Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 4
Submit an article Journal homepage
187
Views
3
CrossRef citations to date
0
Altmetric
Articles

The first eigenvalue for a quasilinear Schrödinger operator and its application

Olimpio Hiroshi MiyagakiDepartamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil.Correspondence[email protected]
View further author information
,
Sandra Imaculada MoreiraDepartamento de Matemática e Informática, Universidade Estadual do Maranhão, São Luís, Brazil.View further author information
&
Ricardo RuviaroDepartamento de Matemática, Universidade de Brasília, Brasília, Brazil.View further author information
Pages 499-512 | Received 01 Aug 2016, Accepted 12 Dec 2016, Published online: 04 Jan 2017

References

  • Cheng Y, Yang J. Positive solution to a class of relativistic nonlinear Schrödinger equation. J Math Anal Appl. 2014;411:665–674.
  • Kurihura S. Large-aplitude quasi-solitons in superfluids films. J Phys Soc Jpn. 1981;50:3262–3267.
  • Poppenberg M, Schmitt K, Wang Z-Q. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc Variations. 2002;14:329–344.
  • Liu J-Q, Wang Y-Q, Wang Z-Q. Soliton solutions for quasilinear Schrödinger equations I. Proc Am Math Soc. 2003;131:441–448.
  • Liu J-Q, Wang Y-Q, Wang Z-Q. Soliton solutions for quasilinear Schrödinger equations II. J Differ Equ. 2003;187:473–493.
  • Colim M. Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2. Adv Differ Equ. 2003;8:1–28.
  • Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation: a dual approach. Nonlinear Anal. 2004;56:213–226.
  • do Ó JM, Miyagaki OH, Moreira SI. On a quasilinear Schrödinger problem at resonance. Adv Nonlinear Stud. 2016;16:569–580.
  • Laedke EW, Spatschek KH, Stenflo L. Evolution theorem for a class of perturbed envelope soliton solutions. J Math Phys. 1982;24(12):2764–2769.
  • De Bouard A, Hayashi N, Saut J. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Commun Math Phys. 1997;189:73–105.
  • Shen Y, Wang Y. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal. 2013;80:194–201.
  • Yang J, Wang Y, Abdelgadir AA. Soliton solutions for quasilinear Schrödinger equations. J Math Phys. 2013;54:071502-19pp.
  • Cheng Y, Yang J. The existence result for a relativistic nonlinear Schrödinger equation. J Math Phys. 2015;56:033508-1–033508-12.
  • Cheng Y, Yang J. The Existence and uniqueness result for a relativistic nonlinear Schrödinger equation. Abstract Appl Anal. 2014:362985-10pp.
  • Cheng Y, Yao Y. Soliton solutions to a class of relativistic nonlinear Schrödinger equation. Appl Math Comput. 2015;260:342–350.
  • Deng Y, Peng S, Yan S. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differ Equ. 2015;258:115–147.
  • Deng Y, Peng S, Yan S. Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J Differ Equ. 2016;260:1228–1262.
  • Huang W, Xiang J. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Commun Pure Appl Anal. 2016;15:1309–1333.
  • Crandall M, Rabinowitz P. Bifurcation, perturbation of simple eigenvalues and linearized stability. Arch R Mech Anal. 1973;52:161–180.
  • Alama S, Tarantello G. On semilinear elliptic equations with indefinite nonlinearities. Calc Variations Partial Differ Equ. 1993;1:439–475.
  • Gilbard D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 1983.
  • Benouhiba N, Belyacine Z. On the solutions of the (p, q)-Laplacian problem at resonance. Nonlinear Anal. 2013;77:74–81.
  • Drábek P, Milota J. Methods of nonlinear analysis. Applications to differential equations. Basel: Birkhäuser Verlag AG; 2007.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.