Electron. J. Diff. Eqns., Vol. 2001(2001), No. 31, pp. 1-21.

Potential theory for quasiliniear elliptic equations

A. Baalal & A. Boukricha

Abstract:
We discuss the potential theory associated with the quasilinear elliptic equation
$$ -{\rm div}({\cal A}(x,\nabla u))+{\cal B}(x,u)=0. $$
We study the validity of Bauer convergence property, the Brelot convergence property. We discuss the validity of the Keller-Osserman property and the existence of Evans functions.

Submitted October 24, 2000. Published May 7, 2001.
Math Subject Classifications: 31C15, 35D65, 35J60.
Key Words: Quasilinear elliptic equation, Convergence property, Keller-Osserman property, Evans functions.

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Azeddine Baalal
Departement de Mathematiques et d'Informatique
Faculte des Sciences Ain Chock
Km 8 Route El Jadida B.P. 5366 Maarif
Casablanca, Maroc
e-mail: baalal@facsc-achok.ac.ma
Abderahman Boukricha
Departement de Mathematiques
Faculte des Sciences de Tunis
Campus Universitaire 1060
Tunis, Tunisie
e-mail: aboukricha@fst.rnu.tn

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