In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the appl...In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.展开更多
让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以...让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以及锋利的系数为 S <SUB 的各种各样的子集跳 > k+1 </SUB><SUP>*</SUP>(B) 。展开更多
The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Li...The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex.展开更多
Let f(x) be an almost spirallike mapping of type β with order α on unit ball Bof complex Banach space X. In this paper, we consider the growth and covering theoremsfor f(x), we also prove that the estimation is prec...Let f(x) be an almost spirallike mapping of type β with order α on unit ball Bof complex Banach space X. In this paper, we consider the growth and covering theoremsfor f(x), we also prove that the estimation is precise when β = 0 and still give growth upperbound and distortion upper bound for subordinate mapping. This result include some resultsknown.展开更多
In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almos...In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.展开更多
1. In Ref. [1], Carl H. FitzGerald et al. gave the first result about the growth theorem in several complex variables. They proved that if f is a normalized biholomorphic starlike mapping from the unit ball B^n to C^n,
The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain mus...The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.展开更多
In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R...In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R^N(N > 2), f(x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ_1, λ = λ_?(? = 2, 3, · · ·), and λ_? is the eigenvalues of the operator(-?_N, W_0^(1,N)(?)),which is defined by the Z_2-cohomological index.展开更多
In this paper, we establish the existence of multiple solutions to a class of Kirchhoff type equations involving critical exponent, concave term and critical growth. Our main tools are the Nehari manifold and mountain...In this paper, we establish the existence of multiple solutions to a class of Kirchhoff type equations involving critical exponent, concave term and critical growth. Our main tools are the Nehari manifold and mountain pass theorem.展开更多
基金Supported by the Doctoral Foundation of Pingdingshan University（PXY-BSQD-20150 05） Supported by the Natural Science Foundation of Zhejiang Province（Y14A010047）+1 种基金 Supported by the the Key Scientific Research Projects in Universities of Henan Province（16Bl10010） Supported by the Foster Foundation of Pingdingshan University（PXY-PYJJ2016007）
文摘In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.
基金Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Nos.19540205,200717540138,2007).
文摘让 B 是在一个复杂 Banach 空格的联合起来的球。让 S <SUB > k+1 </SUB><SUP>*</SUP>(B) 是 B 上的规范的星形的地图砰 f 的家庭以便 0 是的 z = f (z)-z 的零顺序 k+1。作者突然地获得生长和盖住的定理，以及锋利的系数为 S <SUB 的各种各样的子集跳 > k+1 </SUB><SUP>*</SUP>(B) 。
文摘The growth theorem and the 1/2 covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex.
基金Supported by the National Natural Science Foundation of China(10271117)
文摘Let f(x) be an almost spirallike mapping of type β with order α on unit ball Bof complex Banach space X. In this paper, we consider the growth and covering theoremsfor f(x), we also prove that the estimation is precise when β = 0 and still give growth upperbound and distortion upper bound for subordinate mapping. This result include some resultsknown.
基金The research was supported by the National Nat ural Science Foundation of China(10571164)Specialized Research Fund for the Doctoral Program of Higher Education(20050358052)+1 种基金Guangdong Natural Science Foundation(06301315)the Doctoral Foundation of Zhanjiang Normal University(Z0420)
文摘In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.
文摘1. In Ref. [1], Carl H. FitzGerald et al. gave the first result about the growth theorem in several complex variables. They proved that if f is a normalized biholomorphic starlike mapping from the unit ball B^n to C^n,
文摘The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.
基金Supported by Shanghai Natural Science Foundation(15ZR1429500)NNSF of China(11471215)
文摘In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R^N(N > 2), f(x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ_1, λ = λ_?(? = 2, 3, · · ·), and λ_? is the eigenvalues of the operator(-?_N, W_0^(1,N)(?)),which is defined by the Z_2-cohomological index.
文摘In this paper, we establish the existence of multiple solutions to a class of Kirchhoff type equations involving critical exponent, concave term and critical growth. Our main tools are the Nehari manifold and mountain pass theorem.
