Classification results for Kirchhoff equations in RN
Classification results for Kirchhoff equations in RN
Source title:
Complex Variables and Elliptic Equations,
2018
(ISI)
Academic year of acceptance:
2018-2019
Abstract:
We study the Kirchhoff equation of Hardy-Hénon typewhere constants
and a+b>0. We show that this equation has no positive solution if
or
, where
. In the critical case
where
, we provide a necessary and sufficient conditions on a and b for the equation to have positive solutions and we classify all such solutions. We also prove the nonexistence of nontrivial stable solutions of the equation in dimension
, where q>3.