Stability and Asymptotic Behavior of the Causal Operator Dynamical Systems Using Nonlinear Variation of Parameters

The operator T from a domain D into the space of measurable functions is called a nonanticipating operator if the past informations is independent from the future outputs. We will use the solution to the operator di§erential equation y0(t) = A(t)y(t)+f(t; y(t); T(y)(t)) to analyze the solution of this operator di§erential equation which is generated by a perturbation (t) = g(t; yt ; T2(yt)). When this perturbation is from a measurable space then the existence and uniqueness of the solution to the operator di§erential equation will be studied. Finally, we use the nonlinear variation of parameters for nonanticipating operator di§erential equations to study the stability and asymptotic behavior of the equilibrium solution