The Study On A Type Of Systems Of Singular Nonlinear Ordinary Differential Equations In The Complex Domain

In science and production, many problems can be attributed to ordinarydifferential equations. Complex nonlinear equations have greatly developed in recentyears, studying the existence and uniqueness of solution to nonlinear ordinarydifferential equations in the complex domain is the most important content for manyresearchers, so it has very important practical significance.In the early twentieth century, W.Walter proved the famous Cauchy-Kowalevskytheorem by constructing contraction mapping operator in a Banach space and usingthe fixed theorem of the functional analysis. Later, when people did research on thesummaries of formal series solutions to analitic partial differential equations, theyfound it could be solved by using the above method to prove the existence anduniqueness of the holomorphicand bounded solution, besides, this method also can beused to prove the existence and uniqueness of the solutions to some systems ofsingular nonlinear ordinary differential equations in the complex domain.By this method, my thesis solves the existence and uniqueness problems of thesolutions to three types of systems of ordinary differential equations in the complexdomain. In the first part, I prove the existence and uniqueness of the solution to aspecific nonlinear ordinary differential equation with complex coefficients andprovide existence fields of the solution; In the second part, I apply the method used inthe first part to a system of generalized differential equation; The last part is furtherapplication of the above method.