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18). If ϕ ∈ C− , it is not difficult to show that x(t, ϕ) → −∞ as t → ∞. As a consequence of these remarks, we discuss this equation in the subset C+ of C. , ϕ). It also is clear that Tα (t) is a bounded map for each t ≥ 0. It is possible to show that, for each ϕ ∈ C+ , there is a t0 (ϕ, α) such that |Tα (t)ϕ|≤ exp α − 1 for t ≥ t0 (ϕ, α). 8); that is, A is compact, invariant and attracts bounded sets of C. 8). Yorke (1970) extended this result (even for more general equations) to the interval 0 < α < 3/2.

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