Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SIX SOLUTIONS FOR THE SEMILINEAR WAVE EQUATION WITH NONLINEARITY CROSSING THREE EIGENVALUES

  • Choi, Q-Heung (Department of Mathematics Education Inha University) ;
  • Jung, Tacksun (Department of Mathematics Kunsan National University)
  • Received : 2012.08.14
  • Accepted : 2012.09.15
  • Published : 2012.09.30
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Abstract

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

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