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A Liouville theorem for the subcritical Lane-Emden system

  • * Corresponding author: Genggeng Huang

    * Corresponding author: Genggeng Huang

The first author is partially supported by NSF DMS-1405175. The second author is partially supported by NSFC-11401376 and the Scholarship of International Postdoctoral Exchange Fellowship Program

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  • The Lane-Emden conjecture says that the subcritical Lane-Emden system admits no positive solution. In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy-type a priori estimate. The necessity of the condition we found can be easily checked. However, a major difficulty lies in the sufficiency. The proof is quite involving, but the benefit is that it reduces the longstanding problem to obtaining the a priori estimate of energy type.

    Mathematics Subject Classification: Primary: 35B09, 35B53, 35J05, 35J61.


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