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

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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.

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Correspondence to Habib Mâagli.

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Mathematics Subject classification (1991): 34B15, 34B27.

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Mâagli, H., Zribi, M. On a New Kato Class and Singular Solutions of a Nonlinear Elliptic Equation in Bounded Domains of \(\mathbb{R}^n\) . Positivity 9, 667–686 (2005). https://doi.org/10.1007/s11117-005-2782-z

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