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

Author

Listed:
  • Shenghui Sun

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830010, China)

  • Fei Han

    (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830010, China)

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.

Suggested Citation

  • Shenghui Sun & Fei Han, 2024. "On the Classification of Entire Solutions to the Critical Lane–Emden Equation," Mathematics, MDPI, vol. 12(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1822-:d:1413201
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