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On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of $\Bbb{R}^n$. (English) Zbl 1131.35335
Summary: Using a new form of the $3 G$-Theorem for the Green function of a bounded domain $\Omega$ in $\Bbb{R}^{n}$, we introduce a new Kato class $K (\Omega)$ which contains properly the classical Kato class $K_{n}(\Omega)$. Next, we exploit the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations.

35J60Nonlinear elliptic equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J25Second order elliptic equations, boundary value problems
Full Text: DOI
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