On the solution of Dirichlet problem of complex Monge-Ampère equation on Cartan-Hartogs domain of the second type

Complex Monge-Ampère equation is a nonlinear equation with high degree, so its solution is very difficult to get. How to get the plurisubharmonic solution of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper. Firstly, the complex Monge-Ampère equation is reduced to a nonlinear second-order ordinary differential equation (ODE) by using quite different method. Secondly, the solution of the Dirichlet problem is given in semi-explicit formula, and under a special case the exact solution is obtained. These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.

Complex Monge-Ampère equation is a nonlinear equation with high degree,so its solution is very diffcult to get.How to get the plurisubharmonic solution of Dirichlet problem of complex Monge- Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper.Firstly,the complex Monge-Ampère equation is reduced to a nonlinear secondorder ordinary differential equation(ODE)by using quite different method.Secondly,the solution of the Dirichlet problem is given in semi-explicit formula,and under a special case the exact solution is obtained.These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.