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Dirichlet problem for quasi-linear elliptic equations

open access: yesElectronic Journal of Differential Equations, 2002
We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x), abla u(x))+mathcal{B}(x,u(x),abla u(x))=0.
Azeddine Baalal, Nedra Belhaj Rhouma
doaj  

Large solutions for an elliptic system of quasilinear equations

open access: yesJournal of Differential Equations, 2008
AbstractIn this paper we consider the quasilinear elliptic system Δpu=uavb, Δpv=ucve in a smooth bounded domain Ω⊂RN, with the boundary conditions u=v=+∞ on ∂Ω. The operator Δp stands for the p-Laplacian defined by Δpu=div(|∇u|p−2∇u), p>1, and the exponents verify a,e>p−1, b,c>0 and (a−p+1)(e−p+1)⩾bc.
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