Applied Mathematics

Volume 8, Issue 12 (December 2017)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.83  Citations  

Variation of Parameters for Causal Operator Differential Equations

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DOI: 10.4236/am.2017.812134    816 Downloads   1,385 Views  Citations


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 tt0 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.

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Ahangar, R. (2017) Variation of Parameters for Causal Operator Differential Equations. Applied Mathematics, 8, 1883-1902. doi: 10.4236/am.2017.812134.

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