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The eigenvalue problem of the complex Monge-Ampère equation. (Chinese. English summary) Zbl 0847.35092

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
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