Nonlinear polyharmonic boundary value problems in the punctured unit ball

In this paper we investigate the existence and the asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of R-n(n >= 3). Our arguments are based on potential theory associated to the polyharmonic operator (-Delta)(m), where m is a positive integer less than n/2, properties of functions in the Kato class K-m,K-n, Karamata regular variation theory tools and the Schauder fixed point theorem.

Automated summary

This paper investigates the existence and asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of R-n(n>=3). The arguments are based on potential theory associated with the polyharmonic operator (-Delta)(m), where m is a positive integer less than n/2, properties of functions in the Kato class K-m, K-n, Karamata regular variation theory tools, and the Schauder fixed point theorem.