Pavel Drabek & Mitsuharu Otani
We prove that the nonlinear eigenvalue problem for the p-biharmonic operator with , and a bounded domain in with smooth boundary, has principal positive eigenvalue which is simple and isolated. The corresponding eigenfunction is positive in and satisfies on , in . We also prove that is the point of global bifurcation for associated nonhomogeneous problem. In the case we give a description of all eigenvalues and associated eigenfunctions. Every such an eigenvalue is then the point of global bifurcation.
Submitted February 9, 2001. Published July 3, 2001.
Math Subject Classifications: 35P30, 34C23.
Key Words: p-biharmonic operator, principal eigenvalue, global bifurcation.
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|Pavel Drabek |
Centre of Applied Mathematics
University of West Bohemia
Univerzitni 22, 306 14 Plzen
|Mitsuharu Otani |
Department of Applied Physics
School of Science and Engineering
3-4-1, Okubo Tokyo, Japan, 169-8555
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