Qu, Changzheng; Cui, Shangbin The eigenvalue problem of the complex Monge-Ampère equation. (Chinese. English summary) Zbl 0847.35092 Pure Appl. Math. 11, No. 2, 37-40 (1995). Summary: We discuss the eigenvalue problem of the complex Monge-Ampère 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. Finally, we study the existence and bifurcation of the solution for a class of complex Monge-Ampère equations by using the existence of the eigenvalue and the eigenfunction. MSC: 35P05 General topics in linear spectral theory for PDEs 35F20 Nonlinear first-order PDEs 30E25 Boundary value problems in the complex plane Keywords:complex Monge-Ampère equation; existence and uniqueness of the eigenvalue problem; complex Laplace operator; bifurcation PDFBibTeX XMLCite \textit{C. Qu} and \textit{S. Cui}, Pure Appl. Math. 11, No. 2, 37--40 (1995; Zbl 0847.35092)