Asymptotics of ground states for fractional H\'enon systems

TL;DR

This paper studies the limiting behavior of positive ground states in fractional Hénon systems as the nonlinearity approaches the critical Sobolev exponent, revealing their asymptotic properties.

Contribution

It provides new insights into the asymptotic behavior of ground states for fractional Hénon systems near criticality, a topic not extensively explored before.

Findings

Characterization of ground state asymptotics near critical exponent

Identification of concentration phenomena in solutions

Extension of classical results to fractional Laplacian context

Abstract

We investigate the asymptotic behavior of positive ground states for H\'enon type systems involving a fractional Laplacian on a bounded domain, when the powers of the nonlinearity approach the Sobolev critical exponent.