We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（...We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2014JM1021)
文摘We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.
