Geodesic
A fixed point method for nonlinear equations involving a duality mapping defined on product spaces
Electronic journal of differential equations, Tome 2013 (2013)
The aim of this paper is to obtain solutions for the equation

$ J_{q,p} (u_1,u_2) =N_{f,g}(u_1,u_2), $

where $J_{q,p}$ is the duality mapping on a product of two real, reflexive and smooth Banach spaces $X_1, X_2$, corresponding to the gauge functions $\varphi_1(t)=t^{q-1}, \varphi_2(t)=t^{p-1}, 1$ 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 Leray-Schauder 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)-pseudo-Laplacian or with $(A_q, A_p)$-Laplacian.
Classification : 58C15, 35J20, 35J60, 35J65
Keywords: duality mapping, Leray-Schauder degree, (q, p)-Laplacian 
@article{EJDE_2013__2013__a7,
     author = {Cringanu,  Jenica and Pasca,  Daniel},
     title = {A fixed point method for nonlinear equations involving a duality mapping defined on product spaces},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.58004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a7/}
}
TY  - JOUR
AU  - Cringanu,  Jenica
AU  - Pasca,  Daniel
TI  - A fixed point method for nonlinear equations involving a duality mapping defined on product spaces
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a7/
LA  - en
ID  - EJDE_2013__2013__a7
ER  - 
%0 Journal Article
%A Cringanu,  Jenica
%A Pasca,  Daniel
%T A fixed point method for nonlinear equations involving a duality mapping defined on product spaces
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a7/
%G en
%F EJDE_2013__2013__a7
Cringanu,  Jenica; Pasca,  Daniel. A fixed point method for nonlinear equations involving a duality mapping defined on product spaces. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a7/