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Using a new form of the 3G-Theorem for the Green function of a bounded domain in R n , we introduce a new Kato class K( ) which contains properly the classical Kato class K n ( ). Next, we exploit the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations.Mathematics Subject Classifications (1991): 34B15, 34B27.

We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of R n (n ≥ 2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions K m,n containing properly the classical Kato class K n . We exploit properties of functions belonging to K m,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m.

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