Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 93, pp. 147.
Variational and topological methods for operator equations
involving duality mappings on OrliczSobolev spaces
George Dinca, Pavel Matei
Abstract:
Let
be a strictly increasing odd
continuous function with
and
,
,
the Nfunction
generated by a. Let
be a bounded open subset of
,
,
a nonnegative quadratic form
involving the only generalized derivatives of order m of the
function
and
,
,
be Caratheodory functions.
We study the problem
where
is the duality mapping on
,
subordinated
to the gauge function a (given by (1.5) and
being the Luxemburg norm on
.
By using the LeraySchauder topological degree and the mountain pass theorem
of Ambrosetti and Rabinowitz, the existence of nontrivial solutions is
established. The results of this paper generalize the existence results for
Dirichlet problems with pLaplacian given in [12] and [13].
Submitted June 4, 2007. Published June 21, 2007.
Math Subject Classifications: 35B38, 35B45, 47J30, 47H11.
Key Words: A priori estimate; critical points; OrliczSobolev spaces;
LeraySchauder topological degree; Duality mapping;
Nemytskij operator; Mountain Pass Theorem.
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George Dinca
Faculty of Mathematics and Computer Science,
University of Bucharest
14, Academiei Str., 010014 Bucharest, Romania
email: dinca@fmi.unibuc.ro


Pavel Matei
Faculty of Mathematics and Computer Science,
University of Bucharest
14, Academiei Str., 010014 Bucharest, Romania
email: pavel.matei@gmail.com

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