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On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of n . (English) Zbl 1131.35335
Summary: Using a new form of the 3G-Theorem for the Green function of a bounded domain Ω in 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.
MSC:
35J60Nonlinear elliptic equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J25Second order elliptic equations, boundary value problems
References:
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