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| Complex Monge-Amp`ere equation is a nonlinear equation with high degree,
therefore to get its solution is very difficult. In present paper how to get the solution
of Dirichlet’s problem of Complex Monge-Amp`ere equation on the Cartan-Hartogs domain
of the first type is discussed by using the analytic method. Firstly, the complex
Monge-Amp`ere equation is reduced to the nonlinear ordinary differential equation, then
the solution of the Dirichlet’s problem of complex Monge-Amp`ere equation is reduced to
the solution of two point boundary value problem of the nonlinear second-order ordinary
differential equation. Secondly, the solution of the Dirichlet’s problem is given in semiexplicit
formula, and under the special case the exact solution is obtained. These results
may be helpful for the numerical method of Dirichlet’s problem of complex Monge-Amp`ere
equation on the Cartan-Hartogs domain. |
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| Keywords:Complex Complex Monge-Amp`ere equation, Dirichlet’s problem,Cartan-Hartogs domain, Kaehler-Einstein metric. |
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