Yanyan GUO
. NONEXISTENCE AND SYMMETRY OF SOLUTIONS TO SOME FRACTIONAL LAPLACIAN EQUATIONS IN THE UPPER HALF SPACE[J]. Acta mathematica scientia, Series B, 2017
, 37(3)
: 836
-851
.
DOI: 10.1016/S0252-9602(17)30040-1
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where 0 < α < 2, R+n:={x=(x1, x2,…, xn)|xn > 0}. When K is strictly decreasing with respect to|x'|, the symmetry of positive solutions is proved, where x'=(x1, x2, …, xn-1) ∈ Rn-1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.