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Positivity

, Volume 9, Issue 4, pp 667–686 | Cite as

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

  • Habib Mâagli
  • Malek Zribi
Article

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 K n (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 function positive solution Schauder fixed point theorem singular nonlinear elliptic equation singular solution 

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Copyright information

© Springer 2005

Authors and Affiliations

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

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