Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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AT LEAST TWO SOLUTIONS FOR THE SEMILINEAR BIHARMONIC BOUNDARY VALUE PROBLEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choiy, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2014.08.25
  • Accepted : 2014.11.10
  • Published : 2014.12.30
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Abstract

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

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References

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