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Pseudo almost periodic solutions of some delay differential equations. (English) Zbl 0858.34055
The theory of exponential dichotomy is used successfully to establish the existence of pseudo almost periodic solutions of delay-differential equations of the form x ' (t)=L(t)x t +f(t), tσ, x σ =φ, where (σ,φ)×C([-r,0], n ), r>0, which have pseudo almost periodic coefficients. Also the following theorem is proved: If σ(A)i=ϕ and f: n is continuous and pseudo almost periodic, where σ(A) is the spectrum of the infinitesimal generator A, then x ' (t)=Lx t +f(t) has a unique bounded solution which is also pseudo almost periodic.
34K14Almost and pseudo-periodic solutions of functional differential equations
34C27Almost and pseudo-almost periodic solutions of ODE