Variation of Parameters for Causal Operator Differential Equations

• 作者: Reza R. Ahangar
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Nonlinear OPERATOR Differential EQUATIONS (NODE) Variation of Parameters Nonanticipating (Causal) Alekseev THEOREM
• 年，卷（期）: 2017,（12）
• 页码范围: 1883-1902
• 页数: 20页
• 分类号: O1

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.