@article{f5548fcf9893429ebd37714b043af0d3,

title = "Uniqueness of positive solutions to some coupled cooperative variational elliptic systems",

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 lin-earized 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.",

author = "Yulian An and Chern, {Jann Long} and Junping Shi",

note = "Funding Information: Received by the editors April 10, 2016, and, in revised form, January 16, 2017. 2010 Mathematics Subject Classification. Primary 34C10, 35B05, 35J47, 35J91. 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. Funding Information: 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. The authors thank Professor Chang-Shou Lin for his helpful discussions regarding this project. The authors also thank two anonymous reviewers for their helpful comments which improved the manuscript. This work was done during several visits by J.-P. Shi to the National Center for Theoretical Sciences (NCTS) at National Tsing-Hua University and National Central University (2007, 2010, 2013, 2014), and the visit of Y.-L. An (2014) and J.-L. Chern (2008, 2012) to the College of William and Mary. They thank these institutes for their hospitality and support. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

month = jul,

doi = "10.1090/tran/7207",

language = "English",

volume = "370",

pages = "5209--5243",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "7",

}