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Uniqueness of positive solutions to some coupled cooperative variational elliptic systems


Authors: Yulian An, Jann-Long Chern and Junping Shi
Journal: Trans. Amer. Math. Soc. 370 (2018), 5209-5243
MSC (2010): Primary 34C10, 35B05, 35J47, 35J91
DOI: https://doi.org/10.1090/tran/7207
Published electronically: March 20, 2018
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Abstract: The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to linearized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.


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Additional Information

Yulian An
Affiliation: Department of Mathematics, Shanghai Institute of Technology, Shanghai, 201418, People’s Republic of China
Email: an_yulian@sit.edu.cn

Jann-Long Chern
Affiliation: Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China
Email: chern@math.ncu.edu.tw

Junping Shi
Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795
Email: jxshix@wm.edu

DOI: https://doi.org/10.1090/tran/7207
Received by editor(s): April 10, 2016
Received by editor(s) in revised form: January 16, 2017
Published electronically: March 20, 2018
Additional Notes: The first author was partially supported by Natural Science Foundation of China (11271261, 11772203) and Natural Science Foundation of Shanghai (17ZR1430000).
The second author was partially supported by MOST of Taiwan under grant no. MOST-104-2115-M-008-010-MY3.
The third author was partially supported by US-NSF grants DMS-1022648 and DMS-1313243.
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