Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GEOMETRIC RESULT FOR THE ELLIPTIC PROBLEM WITH NONLINEARITY CROSSING THREE EIGENVALUES

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2012.11.08
  • Accepted : 2012.12.10
  • Published : 2012.12.30
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Abstract

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the 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 axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

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Acknowledgement

Supported by : Inha University

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