Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 86, pp. 1-10.

Title: Entire solutions of semilinear elliptic equations

Authors: Alexander Gladkov (Vitebsk State Univ., Belarus)
         Nickolai Slepchenkov (Vitebsk State Univ., Belarus)
 
Abstract: 
  We consider existence of entire  solutions of a semilinear elliptic
  equation $\Delta u= k(x) f(u)$ for $x \in \mathbb{R}^n$,
  $n\ge3$. 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. 

Submitted November 3, 2003. Published June 23, 2004.
Math Subject Classifications: 35J60.
Key Words: Semilinear elliptic equation; entire solutions; nonexistence.