Infinitely many solutions for a fourth-order elastic beam equation

Article

Abstract

Existence results of infinitely many solutions for a fourth-order nonlinear boundary value problem are established. No symmetric condition on the nonlinear term is assumed. The main tool is an infinitely many critical points theorem.

Mathematics Subject Classification (2000)

34B15 58E05 

Keywords

Fourth-order equations Critical points Infinitely many solutions 

References

  1. 1.
    Bai Z., Wang H.: On positive solutions of some nonlinear fourth-order beam equations. J. Math. Anal. Appl. 270, 357–368 (2002)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bonanno, G., Molica Bisci, G.: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Bound. Value Probl. 1–20 (2009)Google Scholar
  3. 3.
    Bonanno G., Di Bella B.: A boundary value problem for fourth-order elastic beam equations. J. Math. Anal. Appl. 343, 1166–1176 (2008)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Cabada A., Cid J. A., Sanchez L.: Positivity and lower and upper solutions for fourth order boundary value problems. Nonlinear Anal. 67, 1599–1612 (2007)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Grossinho M.R., Sanchez L., Tersian S.A.: On the solvability of a boundary value problem for a fourth-order ordinary differential equation. Appl. Math. Lett. 18, 439–444 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Han G., Xu Z.: Multiple solutions of some nonlinear fourth-order beam equations. Nonlinear Anal. 68, 3646–3656 (2008)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Liu X.-L., Li W.-T.: Existence and multiplicity of solutions for fourth-order boundary values problems with three parameters. Math. Comput. Model. 46, 525–534 (2007)MATHCrossRefGoogle Scholar
  8. 8.
    Liu X.-L., Li W.-T.: Existence and multiplicity of solutions for fourth-order boundary values problems with parameters. J. Math. Anal. Appl. 327, 362–375 (2007)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Ricceri B.: A general variational principle and some of its applications. J. Comput. Appl. Math. 113, 401–410 (2000)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Science for Engineering and Architecture (Mathematics Section), Engineering FacultyUniversity of MessinaMessinaItaly

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