# American Institute of Mathematical Sciences

January  2018, 17(1): 85-112. doi: 10.3934/cpaa.2018006

## Liouville results for fully nonlinear integral elliptic equations in exterior domains

 Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

* Corresponding author

Received  January 2017 Revised  June 2017 Published  September 2017

Fund Project: Y. Wang is supported by NSFC, No: 11661045.

In this paper, we obtain Liouville type theorems both in the whole space and exterior domain in viscosity sense for fully nonlinear elliptic inequality involving nonlocal Pucci's operator. The nonlocal property of the operator, we only have a much weaker comparison principle, compared with the inequality with classical Pucci's operators, which give rise to the difficulties for the Hadamard type property in exterior domain.

Citation: Hongxia Zhang, Ying Wang. Liouville results for fully nonlinear integral elliptic equations in exterior domains. Communications on Pure & Applied Analysis, 2018, 17 (1) : 85-112. doi: 10.3934/cpaa.2018006
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