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On a transcendental equation involving quotients of Gamma functions


Authors: Senping Luo, Juncheng Wei and Wenming Zou
Journal: Proc. Amer. Math. Soc. 145 (2017), 2623-2637
MSC (2010): Primary 33B15; Secondary 35B35
DOI: https://doi.org/10.1090/proc/13408
Published electronically: December 15, 2016
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Abstract: This note is aimed at giving a complete characterization of the following equation in $ p$:

$\displaystyle \displaystyle p\frac {\Gamma (\frac {n}{2}-\frac {s}{p-1})\Gamma ... ...1})} =\Big (\frac {\Gamma (\frac {n+2s}{4})}{\Gamma (\frac {n-2s}{4})}\Big )^2.$

The method is based on some key transformations and the properties of the Gamma function. Applications to fractional nonlinear Lane-Emden equations will be given.


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Additional Information

Senping Luo
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China

Juncheng Wei
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada

Wenming Zou
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China

DOI: https://doi.org/10.1090/proc/13408
Received by editor(s): June 21, 2016
Received by editor(s) in revised form: August 1, 2016
Published electronically: December 15, 2016
Additional Notes: This work was supported by NSFC of China and NSERC of Canada
Communicated by: Mourad Ismail
Article copyright: © Copyright 2016 American Mathematical Society