On the Hardy-Sobolev equation

TL;DR

This paper investigates the Hardy-Sobolev equation in higher dimensions and bounded domains, transforming the problem to analyze bifurcation of radial solutions at specific parameter values.

Contribution

It introduces a transformation that removes the singular term, enabling bifurcation analysis of positive solutions in the Hardy problem.

Findings

Bifurcation results for radial positive solutions

Explicit parameter values where bifurcations occur

Transformation method simplifying the Hardy problem

Abstract

In this paper we study the Hardy problem in R^N with N>2 and in a ball B of R^N. Using a suitable map we transform the Hardy problem into another one without the singular term. Then we obtain some bifurcation results from the radial positive solutions corresponding to some explicit values of the parameter lambda.