Abstract
In this paper, we obtain symmetry and monotonicity of positive solutions for the systems involving uniformly elliptic nonlocal operators in a domain (bounded or unbounded) in \(R^n\) using a direct method of moving planes. Our results include subcritical case, critical case and supercritical case and seem to be the first symmetric properties of the system involving uniformly elliptic nonlocal operators and containing the gradient of the solutions in the nonlinear terms.
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Acknowledgements
The author would like to express sincere thanks to the anonymous referee and editors for their valuable suggestions and comments which greatly improve the quality of the paper. This work is supported by NSFC 11971415 and Nanhu Scholars Program for Young Scholars of XYNU (Grant no. 2019).
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Zeng, F. Symmetric Properties for System Involving Uniformly Elliptic Nonlocal Operators. Mediterr. J. Math. 17, 79 (2020). https://doi.org/10.1007/s00009-020-01514-6
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DOI: https://doi.org/10.1007/s00009-020-01514-6