Abstract
In this article, we study nonlinear systems involving several p-Laplacian operators with variable coefficients. We consider the system
-Delta(pi) u(i) = a(ii)(x)vertical bar u(i)vertical bar(pi-2)u(i) - Sigma(n)(j not equal i) a(ij)(x)vertical bar u(i)vertical bar(alpha i) vertical bar u(j)vertical bar(alpha j) u(j) + f(i)(x),
where Delta(p) denotes the p-Laplacian defined by Delta(p)u equivalent to div[vertical bar del u vertical bar(p-2) del(u)] with p > 1, p not equal 2; alpha(i) >= 0; f(i) are given functions; and the coefficients a(ij)(x) (1 <= i, j <= 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.