On the Classification of Entire Solutions to the Critical Lane–Emden Equation

Abstract

The positive solutions to the critical Lane–Emden equation in Rn have been classified completely by the moving plane method. Afterwards, with additional conditions such as limited energy or volume, there is proof that relies entirely on integration by parts and inequalities techniques. In this paper, the authors provide a new approach to obtain the same classification results without further assumptions.

Keywords

• critical Lane–Emden equation
• entire solution
• integral estimate
• integration by parts