Bulletin of the Australian Mathematical Society

Research Article

EXISTENCE OF POSITIVE EVANESCENT SOLUTIONS TO SOME QUASILINEAR ELLIPTIC EQUATIONS

OCTAVIAN G. MUSTAFAa1 p1

a1 Faculty of Mathematics, D.A.L., University of Craiova, Romania (email: octaviangenghiz@yahoo.com)

Abstract

We establish that the elliptic equation

\[ \Delta u+f(x,u)+g(\vert x\vert )x\cdot \nabla u=0, \]

defined in an exterior domain of xs211Dn, n≥3, has a positive solution which decays to 0 as $\vert x\vert \rightarrow +\infty $ under quite general assumptions upon f and g.

(Received October 15 2007)

2000 Mathematics subject classification

  • 34A12;
  • 35J60

Keywords and phrases

  • positive solution;
  • nonlinear elliptic equation;
  • exterior domain

Correspondence:

p1 Corresponding address: Str. Tudor Vladimirescu, Nr. 26, 200534 Craiova, Romania

Footnotes

The author’s research was financed by Romanian AT grant 97GR/25.05.2007 with CNCSIS code 100.