Uniqueness theorem for integral equations and its application
Uniqueness theorem for integral equations and its application
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DOI：
10.1016/j.jfa.2007.03.005
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发表时间：
2007-06
影响因子：
1.7
通讯作者：
Xingwang Xu
中科院分区：
文献类型：
--
作者：
Xingwang Xu
本文致力于回答Y.李关于几何有趣的积分方程。主要结果是给出了参数的一个充要条件，使本文讨论的含参数积分方程有正则解。在满足这种条件的情况下，我们将写出精确解。作为本文方法的应用，我们证明了Sn上给定数量曲率方程解的不存在性理论可以推广到Sn上给定Branson-Paneitz Q-曲率方程解的不存在性理论。
This paper is devoted to answering a question asked recently by Y. Li regarding geometrically interesting integral equations. The main result is to give a necessary and sufficient condition on the parameters so that the integral equation with parameters to be discussed in this paper have regular solutions. In the case such condition is satisfied, we will write down the exact solution. As its application of our method, we should show that the non-existence theory of the solutions of prescribed scalar curvature equation on Sncan be generalized to that of prescribed Branson–Paneitz Q-curvature equations on Sn.