Existence of entire solutions for semilinear elliptic systems under the Keller-Osserman condition

Abstract

Under the Keller-Osserman condition on $f+g$, we show the existence and nonexistence of entire solutions for the semilinear elliptic system $Delta u =p(x)f(v), quad Delta v =q(x)g(u),quad xin mathbb{R}^N$, where $p,q:mathbb{R}^No [0,infty)$ are continuous functions.

Keywords

• Semilinear elliptic systems
• entire solutions
• existence