Existence of entire positive kk-convex radial solutions to Hessian equations and systems with weights

Under the simple conditions on ff and gg, we show that entire positive kk-convex radial solutions exist for the Hessian equation σk(λ(D2u))=p(|x|)f(u),x∈RN and system σk(λ(D2u))=p(|x|)f(v),σk(λ(D2v))=q(|x|)g(u),x∈RN, where p,q:[0,∞)→(0,∞)p,q:[0,∞)→(0,∞) are continuous.