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

Shenghui Sun and Fei Han ()
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Shenghui Sun: School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830010, China
Fei Han: School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830010, China

Mathematics, 2024, vol. 12, issue 12, 1-9

Abstract: The positive solutions to the critical Lane–Emden equation in R n 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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