Entire solutions of semilinear elliptic equations

Abstract

We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors. We prove a certain optimality of these results and new sufficient conditions for the nonexistence of entire solutions.

Keywords

• Semilinear elliptic equation
• entire solutions
• nonexistence.