Asymptotic Behavior of Singular Solution to the k-Hessian Equation with a Matukuma-Type Source

Abstract

This paper is concerned with radially positive solutions of the [see formula in PDF]-Hessian equation involving a Matukuma-type source [see formula in PDF], where [see formula in PDF] is the [see formula in PDF]-Hessian operator, [see formula in PDF], and [see formula in PDF] is a suitable bounded domain in [see formula in PDF]. It turns out that there are two different types of radially positive solutions for [see formula in PDF], i.e., M-solution (singular at [see formula in PDF]) and E-solution (regular at [see formula in PDF]), which is distinct from the case when [see formula in PDF]. For [see formula in PDF], we apply an iterative approach to improve accuracy of asymptotic expansions of M-solution step by step to the desired extend. In contrast to the case [see formula in PDF], we require a more precise range of parameters due to repeated application of Taylor expansions, which also makes asymptotic expansions need more delicate investigation.