Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms

Abstract

We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, for on and . We establish the conditions on that ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition on is simple and different to the Keller-Osserman condition.