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Hale, J., Arrieta, J. and Carvalho, A.N. (1992) A Damped Hyperbolic Equation with Critical Exponent. Communications in Partial Differential Equations, 17, 841-866.

has been cited by the following article:

• TITLE: Variation of Parameters for Causal Operator Differential Equations

  AUTHORS: Reza R. Ahangar

  KEYWORDS: Nonlinear Operator Differential Equations (NODE), Variation of Parameters, Nonanticipating (Causal), Alekseev Theorem

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 29, 2017

  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 (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.