复Monge－Ampere方程的特征值问题

THE EIGENVALUE PROBLEM OF THE COMPLEX MONGE-AMPERE EQUATION

讨论了复空间中强拟凸域上的复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的特征值问题，证明了特征值问题解的存在唯一性，并给出了这个特征值与一类复空间中复Ｌａｐｌａｃｅ算子的第一特征值的关系，最后利用特征值及特征函数的存在性讨论了一类复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的解的存在性及其分歧．

This paper discuss the eigenvalue problem of the complex Monge-Ampere equation on strong pseudoconvex domains, and prove the existence and uniqueness of the eigenvalue problem. The relation between the eigenvalue and the first eigenvalue of the complex Laplace operator on the complex domain is presented. In the last, We study the existence and bifurcation of the solution for a class of complex Monge-Ampere equations by using the existence of the eigenvalue and the eigenfunction.