Electron. J. Diff. Eqns., Vol. 2004(2004), No. 86, pp. 1-10.

Entire solutions of semilinear elliptic equations

Alexander Gladkov, Nickolai Slepchenkov

Abstract:
We consider existence of entire solutions of a semilinear elliptic equation
$\Delta u= k(x) f(u)$ for $x \in \mathbb{R}^n$, $n\ge 3$.
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.

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Alexander Gladkov
Mathematics Department, Vitebsk State University
Moskovskii pr. 33, 210038 Vitebsk, Belarus
email:gladkov@vsu.by   gladkoval@mail.ru
Nickolai Slepchenkov
Mathematics Department, Vitebsk State University
Moskovskii Pr. 33, 210038 Vitebsk, Belarus
email: slnick@tut.by

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