A Liouville theorem for subcritical Lane-Emden system

Abstract

In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy type of integral estimate on solutions to subcritical Lane-Emden system. To approach the long standing and interesting conjecture, we believe that one plausible path is to refocus on establishing this energy type estimate.

References in corpus (2)

• Sharp criteria of Liouville type for some nonlinear systems
• A degree theory approach for the shooting method

Cited by in corpus (3)

• A Liouville Theorem for a Class of Fractional Systems in ${\mathbb{R}}_{+}^n$
• On the Lane-Emden conjecture
• On the Hardy-Littlewood-Sobolev type systems