In this thesis , the solution of kolmogorov backward differential equations in birth and death process theory has been proved to be well - posedness by using the theories and methods of linear operator co semigroup in functional analysis . and the existence of superior eigenvalue of the coefficient matrix of the equations has been studied by using the theories of positive operator and conjugate operator 論文主要用泛函分析中的線性算子c _ 0半群理論研究生滅過程理論中柯爾莫哥洛夫向后微分方程組解的適定性,及用正算子和共軛算子的理論和一些結(jié)論研究了該方程組系數(shù)矩陣算子的占優(yōu)本征值的存在性問題。