On a singular sublinear polyharmonic problem

Abstract

This paper deals with a class of singular nonlinear polyharmonic equations on the unit ball B in ℝn (n≥2) where the combined effects of a singular and a sublinear term allow us by using the Schauder fixed point theorem to establish an existence result for the following problem: (−Δ)mu=φ(⋅,u)+ψ(⋅,u) in B (in the sense of distributions), u>0, lim⁡|x|→1u(x)/(1−|x|)m−1=0. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions.