Hessian Lane-Emden Type Systems with Measures Involving Sub-natural Growth Terms

We are interested in a class of k-Hessian Lane-Emden type systems with measure data in the “sublinear growth” rate. We give global pointwise estimates of the so-called Brezis-Kamin type in terms of Wolff potentials, which allows us to obtain necessary and sufficient conditions for the existence of positive solutions. The approach allows one to treat other nonlinear elliptic problems, such as equations involving general quasilinear operators and fractional Laplacian.