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Classification results for Kirchhoff equations in RN

Authors: 

Phuong Le, Nhat Vy Huynh and Vu Ho*

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.