Geodesic
Existence of weak solutions for nonlinear systems involving several $p$-Laplacian operators
Electronic Journal of Differential Equations, Tome 2009 (2009).

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

Summary: In this article, we study nonlinear systems involving several p-Laplacian operators with variable coefficients. We consider the system $$ -\Delta _{p_i}u_i=a_{ii}(x)|u_i|^{p_i-2}u_i -\sum_{j\neq i}^{n}a_{ij}(x)|u_i|^{\alpha _i}|u_j|^{\alpha_j}u_j+f_i(x), $$ where $\Delta _p$ denotes the p-Laplacian defined by $\Delta_{p}u\equiv \hbox{div} [|\nabla u|^{p-2}\nabla u]$ with $p>1, p\neq 2; \alpha _i\geq 0; f_i$ are given functions; and the coefficients $a_{ij}(x) ( 1\leq i,j\leq n)$ are bounded smooth positive functions. We prove the existence of weak solutions defined on bounded and unbounded domains using the theory of nonlinear monotone operators.
Classification : 74H20, 35J65
Keywords: existence of weak solution, nonlinear system, p-Laplacian 
@article{EJDE_2009__2009__a21,
     author = {Khafagy, Salah A. and Serag, Hassan M.},
     title = {Existence of weak solutions for nonlinear systems involving several $p${-Laplacian} operators},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a21/}
}
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Khafagy, Salah A.; Serag, Hassan M. Existence of weak solutions for nonlinear systems involving several $p$-Laplacian operators. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a21/