Estimates for the Green function and singular solutions for polyharmonic nonlinear equation (Q1773462)

Summary: We establish a new form of the \(3G\) theorem for polyharmonic Green function on the unit ball of \(\mathbb{R}^n (n\geq 2)\) 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 \(2m\).