# American Institute of Mathematical Sciences

March  2019, 39(3): 1379-1387. doi: 10.3934/dcds.2019059

## Non-existence of positive solutions for a higher order fractional equation

 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

* Corresponding author: Mei Yu

Received  December 2017 Revised  April 2018 Published  December 2018

Fund Project: This work was supported by the National Nature Science Foundation of China (Grant No.11271299 and No.11801446) and the Natural Science Basic Research Plan in Shaanxi Province of China (Program No.2016JM1023 and No.2018JQ1037.).

In this paper, we consider a nonlinear equation involving fractional Laplacian of higher order on the whole space. We establish the equivalence between the pseudo-differential equation and an integral equation by applying the maximum principle and the Liouville theorem. For positive solutions to the equation, we obtained non-existence by applying the method of moving planes.

Citation: Xuewei Cui, Mei Yu. Non-existence of positive solutions for a higher order fractional equation. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1379-1387. doi: 10.3934/dcds.2019059
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