Pavel Drabek & Mitsuharu Otani
Abstract:
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 Czech Republic e-mail: pdrabek@kma.zcu.cz |
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Mitsuharu Otani Department of Applied Physics School of Science and Engineering Waseda University 3-4-1, Okubo Tokyo, Japan, 169-8555 e-mail: otani@mn.waseda.ac.jp |
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