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Boundary Blow-up Solutions to Nonlocal Elliptic Systems of Cooperative Type

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Abstract

In this paper, we consider the boundary blow-up solutions to the nonlocal elliptic systems of cooperative type. By introducing the boundary measure, the boundary blow-up problem becomes a Cauchy problem. Then using the super-subsolution method, we obtain the existence and nonexistence of positive solutions. Moreover, we study the stability of the minimal solution to the Cauchy problem.

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Acknowledgements

H. Chen is supported by National Natural Science Foundation of China, Nos: 11726614 and 11661045, and by the Jiangxi Provincial Natural Science Foundation, No: 20161ACB20007, and by project of Jiangxi Education Department, No: GJJ160297. G. Lv is supported by National Natural Science Foundation of China, No: 11771123, and Science and Technology Research Key Projects of the Education Department of Henan Province 2015GGJS-024, the Project Funded by China Postdoctoral Science Foundation Nos. 2016M600427 and 2017T100385, and Postdoctoral Science Foundation of Jiangsu Province (Grant No. 1601141B).

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Authors and Affiliations

  1. Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, Jiangxi, People’s Republic of China

    Huyuan Chen

  2. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA

    Jinqiao Duan

  3. Institute of Applied Mathematics, Henan University, Kaifeng, 475001, Henan, People’s Republic of China

    Guangying Lv

Authors
  1. Huyuan Chen
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  2. Jinqiao Duan
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  3. Guangying Lv
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Correspondence to Guangying Lv.

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Communicated by Nader Masmoudi.

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Chen, H., Duan, J. & Lv, G. Boundary Blow-up Solutions to Nonlocal Elliptic Systems of Cooperative Type. Ann. Henri Poincaré 19, 2115–2136 (2018). https://doi.org/10.1007/s00023-018-0668-4

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