Abstract and Applied Analysis

On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem

Aixia Qian and Shujie Li

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Abstract

By means of Minimax theory, we study the existence of one nontrivial solution and multiple nontrivial solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 6 (2005), 673-683.

Dates
First available in Project Euclid: 3 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1128345945

Digital Object Identifier
doi:10.1155/AAA.2005.673

Mathematical Reviews number (MathSciNet)
MR2202955

Zentralblatt MATH identifier
1128.35037

Citation

Qian, Aixia; Li, Shujie. On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem. Abstr. Appl. Anal. 2005 (2005), no. 6, 673--683. doi:10.1155/AAA.2005.673. https://projecteuclid.org/euclid.aaa/1128345945


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References

  • K. C. Chang, Critical Point Theory and Its Applications, Modern Mathematics Series, Shanghai Scientific and Technology Press, Shanghai, 1986.
  • D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren der Mathematischen Wissenschaften, vol. 224, Springer-Verlag, Berlin, 1983.
  • A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis, SIAM Rev. 32 (1990), no. 4, 537--578.
  • A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal. 31 (1998), no. 7, 895--908.
  • --------, Nontrivial solutions for some fourth order semilinear elliptic problems, Nonlinear Anal. 34 (1998), no. 4, 509--523.
  • P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics, vol. 65, American Mathematical Society, Rhode Island, 1986.
  • M. Schechter and K. Tintarev, Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems, Bull. Soc. Math. Belg. Sér. B 44 (1992), no. 3, 249--261.
  • G. Tarantello, A note on a semilinear elliptic problem, Differential Integral Equations 5 (1992), no. 3, 561--565.
  • M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications, vol. 24, Birkhäuser Boston, Massachusetts, 1996.