Abstract

We study systems of two elliptic equations, with right-hand sides with general power-like superlinear growth, and left-hand sides which are of Isaac's or Hamilton-Jacobi-Bellman type (however our results are new even for linear left-hand sides). We show that, under appropriate growth conditions, such sys-tems have positive solutions in bounded domains, and that all such solutions are bounded in the uniform norm. We also get nonexistence results in unbounded domains.