Existence of positive solutions to semilinear elliptic systems with supercritical growth
ABSTRACT We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well known model examples such as systems of the Henon, Lane Emden, and stationary Schrodinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.