Abstract
We study the Maximum Principle and existence of positive weak solutions for the n x n nonlinear elliptic system
-Delta(P,v)u(i) = Sigma(n)(j=1) a(ij)(x) vertical bar u(j)vertical bar(p-2)u(j) + f(i)(x, u(1),u(2),..., u(n)) in Omega u(i) = 0, i = 1, 2,...n n
where the degenerated p-Laplacian defined as Delta(P,p)u = div [P(x)vertical bar del u vertical bar(p-2)del u] with p>1, p not equal 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using "sub-super solutions method".