Liouville-type theorems for elliptic inequalities involving the Δλ-Laplace operator

We establish Liouville-type theorems for the elliptic system of inequalities {-Delta(lambda)u >= v(p), x is an element of R-N, -Delta(lambda)v >= u(q), x is an element of R-N, Here p, q > 0 satisfy some growth conditions, and Delta(lambda) is the strongly degenerate operator of the form Delta(lambda) := (N)Sigma(i=1) partial derivative(xi)(lambda(2)(i)partial derivative(xi)), where lambda = (lambda(1), ... , lambda N) : RN -> RN satisfies some certain conditions. As a direct consequence, we also obtain the Liouville-type theorem for the following elliptic inequality -Delta(lambda)u >= u(p) in R-N.