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Variation of Parameters for Causal Operator Differential Equations
Mathematics Department, Texas A & M University Kingsville, Kingsville, USA
- 1 Mathematics Department, Texas A & M University Kingsville, Kingsville, USA
Applied Mathematics·Volume 08 (2017)·Pages 1883–1902·Published 4 December 2017·DOI10.4236/am.2017.812134
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Abstract
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 ( t 0 , x 0 ) . The initial information is described x (t) = φ ( t) for almost all t ≤ t 0 and φ ( t 0) = φ 0 . We will study the nonlinear variation of parameters (NVP) for this type of nonanticipating operator differential equations and develop Alekseev type of NVP.
KeywordsNonlinear Operator Differential Equations (NODE)Variation of ParametersNonanticipating (Causal)Alekseev Theorem
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