Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

MULTIPLICITY RESULTS FOR SOME FOURTH ORDER ELLIPTIC EQUATIONS

  • Jin, Yinghua (School of Sciences Jiangnan University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2010.11.16
  • Accepted : 2010.12.15
  • Published : 2010.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we consider the Dirichlet problem for an fourth order elliptic equation on a open set in $R^N$. By using variational methods we obtain the multiplicity of nontrivial weak solutions for the fourth order elliptic equation.

Keywords

Acknowledgement

Supported by : Jiangnan University

References

  1. Q.H. Choi and Yinghua Jin, Nonlinearity and nontrivial solutions of fourth order semilinear elliptic equations, Int. J. Appl. Math. Anal. Appl.,29 (2004), 224-234.
  2. Q.H. Choi, T. Jung and P.J. McKenna, The study of a nonlinear suspension bridge equation by a variational reduction method, J. Appl. Anal., 50 (1993), 71-90.
  3. Amir Moradifam, On the critical dimension of a fourth order elliptic problem with negative exponent, J. Differential Equations 248 (2010), 594-616. https://doi.org/10.1016/j.jde.2009.09.011
  4. Tacksun Jung and Q-Heung Choi, Existence of four solutions of some nonlinear hamiltonian system, Hindawi publishing corporation Boundary value problems (2008).
  5. A.M. Micheletti and A.Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal., 31(1998), 895-903. https://doi.org/10.1016/S0362-546X(97)00446-X
  6. P.J. McKenna and W. Walter, Global bifurcation and a Theorem of Tarantello, J. Math. Anal. Appl. 181 (1994), 648-655. https://doi.org/10.1006/jmaa.1994.1049
  7. A.M. Micheletti and C. Saccon, Multiple nontrivial solutions for a floating beam via critical point theory. J. Differential Equations 170 (2001), 157-179. https://doi.org/10.1006/jdeq.2000.3820
  8. S. Li and A. Squlkin, Periodic solutions of an asymptotically linear wave equation, Nonlinear Anal. 1 (1993), 211-230.
  9. J.Q. Liu, Free vibrations for an asymmetric beam equation, Nonlinear Anal. 51.
  10. Tarantello G, A note on a semilinear elliptic problem, Differential Integral Equations 5 (1992), 561-566.