Abdesslem Ayoujil, Abdel Rachid El Amrouss
Abstract:
In this article, we consider the nonlinear eigenvalue problem
where
is a bounded domain in
with smooth
boundary and
are
continuous functions. Considering different situations concerning
the growth rates involved in the above quoted problem, we prove the
existence of a continuous family of eigenvalues. The proofs of the
main results are based on the mountain pass lemma and Ekeland’s
variational principle.
Submitted October 6, 2010. Published February 9, 2011.
Math Subject Classifications: 35G30, 35K61, 46E35.
Key Words: Fourth order elliptic equation; eigenvalue;
Navier condition; variable exponent; Sobolev space;
mountain pass theorem; Ekeland’s variational principle.
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Abdesslem Ayoujil University Mohamed I, Faculty of sciences Department of Mathematics, Oujda, Morocco email: abayoujil@yahoo.fr | |
Abdel Rachid El Amrouss University Mohamed I, Faculty of sciences Department of Mathematics, Oujda, Morocco email: elamrouss@fso.ump.ma |
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