The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind

被引：12

作者：

Wang, Na ^{[1
]}

Wang, Jihua ^{[1
]}

Xiao, Dongmei ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 02期

关键词：

The exact bounds; The number of zeros; Hyperelliptic integrals; The first kind; Chebyshev; ELLIPTIC INTEGRALS; ABELIAN-INTEGRALS; NON-OSCILLATION; DEGREE-4; PERTURBATIONS; PROPERTY; LOOP;

D O I：

10.1016/j.jde.2012.07.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study three classes of complete hyperelliptic integrals of the first kind, which are some degenerate subfamilies of a family considered in the work of Gavrilov and Him It is shown that the three classes of complete hyperelliptic integrals are Chebyshev, and the exact bounds on the number of zeros of these Abelian integrals are one. This result reveals that there exist degenerate subfamilies of ovals of the hyperelliptic Hamiltonian which are not exceptional families proposed by Gavrilov and Iliev, but the corresponding complete hyperelliptic integrals of the first kind still satisfy the Chebyshev property. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：323 / 341

页数：19

共 50 条

[1] Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7
Bakhshalizadeh, A.
Asheghi, R.
Hoseyni, R.
[J]. CHAOS SOLITONS & FRACTALS, 2017, 103 : 279 - 288
[2] Bounds for complete elliptic integrals of the first kind
Andras, Szilard
Baricz, Arpad
[J]. EXPOSITIONES MATHEMATICAE, 2010, 28 (04) : 357 - 364
[3] Complete hyperelliptic integrals of the first kind and their non-oscillation
Gavrilov, L
Iliev, ID
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (03) : 1185 - 1207
[4] MONOTONICITY PROPERTIES AND BOUNDS INVOLVING THE COMPLETE ELLIPTIC INTEGRALS OF THE FIRST KIND
Yang, Zhen-Hang
Qian, Wei-Mao
Chu, Yu-Ming
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2018, 21 (04): : 1185 - 1199
[5] NUMBER OF ZEROS OF COMPLETE ELLIPTIC INTEGRALS
PETROV, GS
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1984, 18 (02) : 148 - 149
[6] On the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
Wu, Juanjuan
Zhang, Yongkang
Li, Cuiping
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 228 : 329 - 335
[7] SHARP BOUNDS OF THE NUMBER OF ZEROS OF ABELIAN INTEGRALS WITH PARAMETERS
Sun, Xianbo
Yang, Junmin
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[8] The Chebyshev's property of certain hyperelliptic integrals of the first kind
Asheghi, R.
Bakhshalizadeh, A.
[J]. CHAOS SOLITONS & FRACTALS, 2015, 78 : 162 - 175
[9] Bounds for complete elliptic integrals of the second kind with applications
Chu, Yu-Ming
Wang, Miao-Kun
Qiu, Song-Liang
Jiang, Yue-Ping
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (07) : 1177 - 1184
[10] Asymptotical bounds for complete elliptic integrals of the second kind
Wang, Miao-Kun
Chu, Yu-Ming
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 402 (01) : 119 - 126

← 1 2 3 4 5 →