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

Abstract EN

We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, Δui+|∇ui|2=pi(|x|)fi(u1,u2,…,ud) for i=1,2,…,d on RN,N≥3 and d∈{1,2,3,…}.

We establish the conditions on pi 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 fi is simple and different to the Keller-Osserman condition.