Entire positive k-convex solutions to k-Hessian type equations and systems

In this paper, we study the existence of entire positive solutions for the k-Hessian type equation S-k(D-2 u + alpha I) = p(vertical bar x vertical bar) f(k) (u), x is an element of R-n and system {S-k(D(2)u + alpha I) = p(vertical bar x vertical bar) f(k) (v), x is an element of R-n, S-k(D(2)v + alpha I) = q(vertical bar x vertical bar)g(k)(u), x is an element of R-n, where D(2)u is the Hessian of u and I denotes unit matrix. The arguments are based upon a new monotone iteration scheme.