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On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of ${ℝ}^{n}$. (English) Zbl 1131.35335
Summary: Using a new form of the $3G$-Theorem for the Green function of a bounded domain ${\Omega }$ in ${ℝ}^{n}$, we introduce a new Kato class $K\left({\Omega }\right)$ which contains properly the classical Kato class ${K}_{n}\left({\Omega }\right)$. Next, we exploit the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations.
##### MSC:
 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. (PDE) 35J25 Second order elliptic equations, boundary value problems
##### References:
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