Thus, we get that { x n } is a Cauchy sequence.
Thus, we get that never takes the value −1, and never takes the value 1.
Thus, we get that f z) is a constant function, which is a contradiction.
For any u in X with ∥ u ∥ X > 1, it follows from (HJ3) that 〈 J ( u ), u 〉 ≥ C ∥ u ∥ X p −. for some positive constant C. Thus we get that 〈 J ( u ), u 〉 ∥ u ∥ X → ∞. as ∥ u ∥ X → ∞ and therefore the operator J is coercive on X.
Thus, we get that ∥ x ¨ n ( t ) ∥ = λ n ∥ f n ( t ) ∥ ≤ ν Θ ˜ ( t ), where ν Θ ˜ ∈ L 1 ( [ 0, T ], [ 0, ∞ ) ) comes from ( 5 i i ), and so { x ¨ n } n is uniformly integrable. This implies that { x ˙ n } n is equi-continuous.
Due to the proportional odds assumption, the impact of age at arrival on HSD and HSG is similar, and thus we get that age at arrival also increases the probability of HSG (except for the 6-9 ate arrivalval category), which is in contrast to the predictions from the multinomial Logit regression (Figures 3c and d).
Thus, we can get that c = k.
Thus, when, one can get, that is,.
Thus, by Lemma 2.4, we get that system (3.29) is dissipative if and only if.
Thus, by Theorem 2.1, we get that f γ has a global error bound.
