Abstract
In this article, we consider the following system involving fully nonlinear nonlocal operators Fα(u(x))+a1(x)v(x)=f(v(x)),Gβ(v(x))+a2(x)u(x)=g(u(x)).Compared to results in Zhang et al. (2020), we apply a narrow region principle and a direct method of moving planes to prove that all positive solutions are radially symmetric about some point in RN under the weaker condition on ai(x) (i=1,2). Furthermore, we obtain the nonexistence of positive solutions for the system on the half space.
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