Variation of Parameters for Causal Operator Differential Equations  

作　　者：Reza R. Ahangar 

机构地区：[1]Mathematics Department, Texas A & M University Kingsville, Kingsville, USA

出　　处：《Applied Mathematics》2017年第12期1883-1902,共20页应用数学（英文）

摘　　要：The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a nonlinear operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t0, x0) . The initial information is described x(t)=φ(t) for almost all t ≤t0 and φ(t0) =φ0. We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.The operator T from a domain D into the space of measurable functions is called a nonanticipating (causal) operator if the past information is independent from the future outputs. We will study the solution x(t) of a nonlinear operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t0, x0) . The initial information is described x(t)=φ(t) for almost all t ≤t0 and φ(t0) =φ0. We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.

关 键 词：Nonlinear OPERATOR Differential Equations (NODE) Variation of Parameters Nonanticipating (Causal) ALEKSEEV THEOREM 

分 类 号：O1[理学—数学]