Korean Journal of Mathematics
- Volume 16 Issue 4
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- Pages.545-551
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- 2008
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- 1976-8605(pISSN)
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- 2288-1433(eISSN)
SOLVABILITY FOR THE PARABOLIC PROBLEM WITH JUMPING NONLINEARITY CROSSING NO EIGENVALUES
- Jung, Tacksun (Department of Mathematics Kunsan National University) ;
- Choi, Q-Heung (Department of Mathematics Education Inha University)
- Received : 2008.11.13
- Published : 2008.12.01
Abstract
We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator
Keywords
- parabolic boundary value problem;
- eigenvalue problem;
- inverse compact operator;
- Lipschitz constant;
- contraction mapping principle;
- complex Hilbert space