whenever n ≥ N. Let f n ( t ) = ( t 2 − α u n ( t ) ) ′ and f ( t ) = ( t 2 − α u ( t ) ) ′. Then (2.4) means that f n → f uniformly on ( 0.1 ], and so lim t → 0 + f ( t ) = lim n → ∞ lim t → 0 + f n ( t ) exists . by applying the theorem to the limit convergence of function sequences again.
Then, there exists such that by applying the intermediate value theorem to (4.21).
Ma and Wang [42] have proved that there exist at least two positive solutions by applying the existence of positive solutions under the fact that is either superlinear or sublinear on by employing the fixed point theorem of cone extension or compression.
This summer, city council took steps toward regulating the 120 or so dispensaries that exist by making them apply for city-issued licenses at a cost of $30,000 [ $21,000USD] for retail shops and $1,000 [$700 USD] for Compassion Clubs.
This summer, city council took steps toward regulating the 120 or so dispensaries that exist by making them apply for city-issued licenses at a cost of $30,000 for retail shops and $1,000 for Compassion Clubs.
Because lim t → 0 + t 2 − α u n ( t ) exists for all n ∈ N, by applying the theorem to the limit convergence of function sequences, we know that lim n → ∞ lim t → 0 + t 2 − α u n ( t ) exists, and lim t → 0 + t 2 − α u ( t ) = lim t → 0 + lim n → ∞ t 2 − α u n ( t ) = lim n → ∞ lim t → 0 + t 2 − α u n ( t ).
Nevertheless, the possibility exists to date different geomorphological processes by applying different dating methods to glacigenic deposits.
In order to solve the problems that exist in the spring safety valve, by applying the iron-nitride magnetic fluid developed by our own efforts to the static sealing techniques, we have successfully developed "the magnetic fluid safety valve for sealing" which was accepted as the state patent in 1999 and authenticated as the achievement in the scientific research in 2000.
By applying Lemma 1.1, there exists at least one solution with period to (1.1).
For sufficiently small by applying Lemma 4.3 there exists a constant such that (4.20).
