Periodic solutions of semilinear functional differential equations in a Hilbert space
The further hypotheses needed are that for each z(t) continuous on [−r,p], the above equation with \(B_i (t,\bar z(t)), B_o (r,\bar z(t),\theta )\) and 0 in place of\(B_i (t,\bar x(t)), B_o (t,\bar x(t),\theta )\) and f(t,xt) has unique solution x ≡ 0, and that A is an operator generating a strongly continuous semigroup which is compact for t > 0.
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