Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 26, pp. 110.
A fixed point method for nonlinear equations involving a duality
mapping defined on product spaces
Jenica Cringanu, Daniel Pasca
Abstract:
The aim of this paper is to obtain solutions for the equation
where
is the duality mapping on a product of two real,
reflexive and smooth Banach spaces
,
corresponding to the
gauge functions
,
,
,
being the Nemytskii operator generated by
the Caratheodory functions f,g which satisfies some appropriate
conditions.
To prove the existence solutions we use a topological method via
LeraySchauder degree.
As applications, we obtained in a unitary manner some existence results
for Dirichlet and Neumann problems for systems with (q,p)Laplacian,
with (q,p)pseudoLaplacian or with
Laplacian.
Submitted July 31, 2012. Published January 27, 2013.
Math Subject Classifications: 58C15, 35J20, 35J60, 35J65.
Key Words: Duality mapping; LeraySchauder degree; (q,p)Laplacian.
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Jenica Cringanu
Department of Mathematics, University of Galati
Str. Domneasca 47, Galati, Romania
email: jcringanu@ugal.ro


Daniel Pasca
Department of Mathematics and Informatics,
University of Oradea
University Street 1, 410087 Oradea, Romania
email: dpasca@uoradea.ro

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