RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

Abstract

Abstract: In this paper, we consider systems of fractional Laplacian equations in Rⁿ with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions u_i in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].

Key words: system of fractional Laplacian, method of moving planes, maximum principles with singular point, Kelvin transform

Congming LI, Zhigang WU. RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN[J].Acta Mathematica Scientia, 2018, 38(5): 1567-1582.

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References

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