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Multiplicity results for some fourth order elliptic equations

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

Abstract

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

참고문헌 (10)

  1. Q.H. Choi, "Nonlinearity and nontrivial solutions of fourth order semilinear elliptic equations", Int. J. Appl. Math. Anal. Appl., 29, pp.224~234 (2004)
  2. Q.H. Choi, "The study of a nonlinear suspension bridge equation by a variational reduction method", J. Appl. Anal., 50, pp.71~90 (1993)
  3. Amir Moradifam, "On the critical dimension of a fourth order elliptic problem with negative exponent", J. Differential Equations, 248, pp.594~616 (2010)
  4. Tacksun Jung, "Existence of four solutions of some nonlinear hamiltonian system" (2008), Hindawi publishing corporation Boundary value problems
  5. A.M. Micheletti, "Multiplicity results for a fourth-order semilinear elliptic problem", Nonlinear Anal., 31, pp.895~903 (1998)
  6. P.J. McKenna, "Global bifurcation and a Theorem of Tarantello", J. Math. Anal. Appl., 181, pp.648~655 (1994)
  7. A.M. Micheletti, "Multiple nontrivial solutions for a floating beam via critical point theory", J. Differential Equations, 170, pp.157~179 (2001)
  8. S. Li, "Periodic solutions of an asymptotically linear wave equation", Nonlinear Anal., 1, pp.211~230 (1993)
  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 Equa-tions, 5, pp.561~566 (1992)

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