Geodesic
A fixed point method for nonlinear equations involving a duality mapping defined on product spaces
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
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     volume = {2013},
     year = {2013},
     language = {en},
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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__a107/