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 equatio...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.展开更多
In this paper,we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph.Using the variation method,we prove that the equation has two distinct solutions under certai...In this paper,we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph.Using the variation method,we prove that the equation has two distinct solutions under certain conditions.展开更多
基金supported by the Research Foundation of Beijing Government(Grant No.YB20081002802)National Natural Science Foundation of China(Grant No.10771144)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No.11721101)by National Key Research and Development Project SQ2020YFA070080.
文摘In this paper,we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph.Using the variation method,we prove that the equation has two distinct solutions under certain conditions.
基金supported by the National Basic Research Program of China (Grant No. 1999075105)the National Natural Science Foundation of China (Grant No. 10471002)Research Foundation for Doctoral Programm (Grant No. 20050574002)
文摘The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
