Linear functional differential equations of neutral type asymptotically autonomous |
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Authors: | A F Izé |
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Institution: | 1. S?o Paulo, Brasil
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Abstract: | Summary It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) (d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying
where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.
Entrata in Redazione il 5 gennaio 1972. |
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