Title: Existence and non-existence results for fully nonlinear elliptic systems

Authors: Alexander Quaas and Boyan Sirakov

Issue: Volume 58 (2009), Issue 2, 751-788

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 systems 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.