Geodesic
Maximum principle and existence of positive solutions for nonlinear systems involving degenerate \(p\)-Laplacian operators
Electronic journal of differential equations, Tome 2007 (2007)
We study the maximum principle and existence of positive solutions for the nonlinear system begingather* -$\Delta $_p,_P$u=a(x)$|u|^p-2$u+b(x)$|u|^alpha|v|^betav+f $\quad $textin $\Omega , \\ -\Delta $_Q,q$v=c(x)$|u|^alpha|v|^beta$u+d(x)$|v|^q-2v+g $\quad $textin $\Omega $, u=v=$0 \quad $texton $\partial \Omega $, endgather* where the degenerate p-Laplacian defined as $\Delta _{p,_{P}}u=\hbox{\rm div}[P(x)|\nabla u|^{p-2}\nabla u]$. We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method.
Classification : 35B50, 35J67, 35J55
Keywords: maximum principle, existence of positive solution, nonlinear elliptic system, degenerated p-Laplacian 
@article{EJDE_2007__2007__a77,
     author = {Khafagy,  Salah A. and Serag,  Hassan M.},
     title = {Maximum principle and existence of positive solutions for nonlinear systems involving degenerate {\(p\)-Laplacian} operators},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1137.35322},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a77/}
}
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%J Electronic journal of differential equations
%D 2007
%V 2007
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%F EJDE_2007__2007__a77
Khafagy,  Salah A.; Serag,  Hassan M. Maximum principle and existence of positive solutions for nonlinear systems involving degenerate \(p\)-Laplacian operators. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a77/