Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} c...Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.展开更多
The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of holomorphic functions on a domain D C C, all of whose zeros have multiplicity at least k, where k ...The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of holomorphic functions on a domain D C C, all of whose zeros have multiplicity at least k, where k 〉 2 is an integer. And let h（z）≠ 0 be a holomorphic function on D. Assume also that the following two conditions hold for every f ∈F： （a） f（z） = 0 [f^（k）（z）｜ 〈 ｜h（z）｜; （b） f^（k）（z）≠ h（z）. Then F is normal on展开更多
The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥...The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h（z） ≠ 0 and oo be a meromorphic function on D. Assume that the following two conditions hold for every f C Dr ： （a） f（z） = 0 =→ ｜f（k）（z）｜ 〈｜h（z）｜. （b） f（k）（z） ≠ h（z）. Then F is normal on D.展开更多
We consider the existence of the ground states solutions to the following Schrodinger equation -△u ＋ V（x）u = f（u）, u ∈ H1（RN）, where N ） 3 and f has critical growth. We generalize an earlier theorem due to ...We consider the existence of the ground states solutions to the following Schrodinger equation -△u ＋ V（x）u = f（u）, u ∈ H1（RN）, where N ） 3 and f has critical growth. We generalize an earlier theorem due to Berestycki and Lions about tile subcritical case to the current critical case.展开更多
基金National Natural Science Foundation of China (Grant No. 11071074)
文摘Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.
基金supported by the National Natural Science Foundation of China (No. 11071074)the Outstanding Youth Foundation of Shanghai (No. slg10015)
文摘The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of holomorphic functions on a domain D C C, all of whose zeros have multiplicity at least k, where k 〉 2 is an integer. And let h（z）≠ 0 be a holomorphic function on D. Assume also that the following two conditions hold for every f ∈F： （a） f（z） = 0 [f^（k）（z）｜ 〈 ｜h（z）｜; （b） f^（k）（z）≠ h（z）. Then F is normal on
基金Project supported by the National Natural Science Foundation of China(No.11071074)the Outstanding Youth Foundation of Shanghai(No.slg10015)
文摘The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D C, all of whose zeros have multiplicity at least k, where k ≥ 2 is an integer. Let h（z） ≠ 0 and oo be a meromorphic function on D. Assume that the following two conditions hold for every f C Dr ： （a） f（z） = 0 =→ ｜f（k）（z）｜ 〈｜h（z）｜. （b） f（k）（z） ≠ h（z）. Then F is normal on D.
文摘We consider the existence of the ground states solutions to the following Schrodinger equation -△u ＋ V（x）u = f（u）, u ∈ H1（RN）, where N ） 3 and f has critical growth. We generalize an earlier theorem due to Berestycki and Lions about tile subcritical case to the current critical case.
