Acta Applicandae Mathematicae

, Volume 115, Issue 3, pp 255–264 | Cite as

Multiplicity of Solutions for Elliptic System Involving Supercritical Sobolev Exponent

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Abstract

The multiplicity of positive solutions are established for a class of elliptic systems involving nonlinear Schrödinger equations with critical or supercritical growth. The solutions are obtained by using Moser iteration technique.

Keywords

Supercritical Sobolev exponent Ljusternik-Schnirelmann theory Moser iteration 

Mathematics Subject Classification (2000)

35Q55 35A15 35B40 

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References

  1. 1.
    Alves, C.O., Figueiredo, G.M., Furtado, M.F.: Multiplicity of solutions for elliptic systems via local mountain pass method. Commun. Pure Appl. Anal. 8, 1745–1758 (2009) MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Alves, C.O.: Local mountain pass for a class of elliptic system. J. Math. Anal. Appl. 335, 135–150 (2007) MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Alves, C.O., Soares, S.H.M.: On the location and profile of spike-layer nodal solutions to nonlinear Schrödinger equations. J. Math. Anal. Appl. 296, 563–577 (2004) MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Alves, C.O., Figueiredo, G.M.: Multiplicity of positive solutions for a quasilinear problem in R N via penalization method. Adv. Nonlinear Stud. 5(4), 551–572 (2005) MathSciNetMATHGoogle Scholar
  5. 5.
    Brézis, H.: Analyse Fonctionnelle-Théorie et applications. Masson, Paris (1983) MATHGoogle Scholar
  6. 6.
    Chabrowski, J., Yang, J.: Existence theorems for elliptic equations involving supercritical Sobolev exponent. Adv. Differ. Equ. 2, 231–256 (1997) MathSciNetMATHGoogle Scholar
  7. 7.
    Chabrowski, J., Yang, J.F.: Multiple semiclassical solutions of the Schrödinger equation involving a critical Sobolev exponent. Port. Math. 57, 3 (2000) 273-284 MathSciNetGoogle Scholar
  8. 8.
    Cingolani, S., Lazzo, M.: Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions. J. Differ. Equ. 160, 118–138 (2000) MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Cingolani, S., Lazzo, M.: Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations, Topol. Methods. Nonlinear Anal. 10, 1–13 (1997) MathSciNetMATHGoogle Scholar
  10. 10.
    Figueiredo, G.M., Furtado, M.F.: Multiple positive solutions for a quasilinear system of Schrödinger equations. Nonlinear Differ. Equ. Appl. 15, 309–333 (2008) MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Figueiredo, G.M.: Multiplicity of solutions for a quasilinear problem with supercritical growth. Electron. J. Differ. Equ. 31, 1–7 (2006) Google Scholar
  12. 12.
    Figueiredo, G.M.: Multiplicidade de soluçes positivas para uma class de prblemas quasilineares. Doct. dissertation, Unicamp (2004) Google Scholar
  13. 13.
    Moser, J.: A new proof de Giorgi’s theorem concerning the regularity problem for elliptic differential equations. Commun. Stat., Simul. Comput. 13, 457–468 (1960) MATHGoogle Scholar
  14. 14.
    Rabelo, P.: On a class of elliptic systems in R N involving supercritical Sobolev exponent. J. Math. Anal. Appl. 354, 46–59 (2009) MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Mathematics, School of Mathematics SciencesNanjing Normal UniversityNanjingPeople’s Republic of China

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