Positivity

, Volume 9, Issue 4, pp 667–686

On a New Kato Class and Singular Solutions of a Nonlinear Elliptic Equation in Bounded Domains of \(\mathbb{R}^n\)

Article

DOI: 10.1007/s11117-005-2782-z

Cite this article as:
Mâagli, H. & Zribi, M. Positivity (2005) 9: 667. doi:10.1007/s11117-005-2782-z

Abstract

Using a new form of the 3G-Theorem for the Green function of a bounded domain Ω in \(\mathbb{R}^{n}\), we introduce a new Kato class K(Ω) which contains properly the classical Kato class Kn(Ω). Next, we exploit the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations.

Keywords

Green functionpositive solutionSchauder fixed point theoremsingular nonlinear elliptic equationsingular solution

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Départment de Mathématiques, Faculté des Sciences de TunisCampus UniversitaireTunisTunisia