Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour
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This paper is devoted to show a variation of constants formula for the operator solution to the non-autonomous retarded differential equation x'(t) = A(t)x(t) + L(t)xt + f(t), xs = φ, t ≥ s ≥ 0, in terms of the inhomogeneous term f, which will allow us to study the asymptotic behaviour of this solution. We treat also the existence of fundamental solutions and the stability of semi-linear retarded differential equations.
CitationBoulite, S., Maniar, L., & Moussi, M. (2003). Non-autonomous retarded differential equations: the variation of constants formulas and the asymptotic behaviour. Electronic Journal of Differential Equations, 2003(62), pp. 1-15.
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