The main result of this paper is presented as follows Let h is homogeneous and symmetric of degree and Then where provided the integrals on the RHS do exists. Some other special cases are also
In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes...In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].展开更多
文摘The main result of this paper is presented as follows Let h is homogeneous and symmetric of degree and Then where provided the integrals on the RHS do exists. Some other special cases are also
基金Supported by National Natural Science Foundation of China-NSAF (10976026)
文摘In this paper, we consider the following integral system： u（x） = R n v q （y） ｜ x y ｜ nα dy, v（x） = R n u p （y） ｜ x y ｜ nμ dy, （0.1） where 0 〈 α, μ 〈 n; p, q ≥ 1. Using the method of moving planes in an integral form which was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions of （0.1） are radially symmetric and decreasing with respect to some point under some general conditions of integrability. The results essentially improve and extend previously known results [4, 8].
