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- W55537154 abstract "The existence of solutions in a weak sense of the following boundary value problem is proved: $$begin{gathered}frac{{dx}}{{dt}} = Axmathop sum limits_{i = 1}^k B_i (t,bar x(t))x(t + omega _i ) + int_{ - underset{raise0.3emhbox{$smash{scriptscriptstyle-}$}}{r} }^o {B_o (t,bar x(t),theta )x} (t + theta )dtheta + f(t,x_t ) hfill x_o = x_p hfill end{gathered}$$where x(t) takes values in a Hilbert space H; $$bar x(t) = (x(t + v_1 ),...,x(t + v_m ), int_{ - underset{raise0.3emhbox{$smash{scriptscriptstyle-}$}}{r} }^o {C(t,theta )x} (t + theta )dtheta ){text{and}}$$C(t,ϑ) is a bounded linear operator on H, uniformly bounded in (t,ϑ); xt is the function on [−r,0] defined by xt(ϑ) = x(t+ϑ); the ωi and νi lie in [−r,0]; p > r > 0; Bi (i=0, …, k) are bounded linear operators on H, uniformly bounded in their arguments, continuous in the second argument in Hm+1 and measurable in t,ϑ; f is a function with values in H, continuous on [0,p] × {continuous functions on [−r,0]} and uniformly bounded." @default.
- W55537154 created "2016-06-24" @default.
- W55537154 creator A5069480667 @default.
- W55537154 date "1980-01-01" @default.
- W55537154 modified "2023-09-27" @default.
- W55537154 title "Periodic solutions of semilinear functional differential equations in a Hilbert space" @default.
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- W55537154 doi "https://doi.org/10.1007/bfb0089307" @default.
- W55537154 hasPublicationYear "1980" @default.
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