带权函数的积分方程组正解的对称性和单调性

Symmetry and monotonicity for a system of integral equations with weight functions

主要研究全空间上一类带权函数的积分方程组正解的径向对称性和单调性问题.在合适条件下,主要利用积分形式的移动平面方法,Hardy-Littlewwood-Sobolev(HLS)和Hlder不等式给出了积分方程组正解的径向对称性和单调性的结论.这一结论很好的推广了已有的结果.

This paper is devoted to the study of radical symmetry and monotonicity of positive solution to a system of integral equations with weight functions. Under some proper assumptions, it has been proved that all the solutions are radial symmetric and monotone decreasing about some point by the method of moving planes integral forms, Hardy-Littewood-Soblev（HLS） and HSlder inequalities. The results complement those derived.