[1]王喜红.一类Abel积分的零点个数估计[J].四川师范大学学报(自然科学版),2019,(05):605-611.[doi:10.3969/j.issn.1001-8395.2019.05.006]
 WANG Xihong.On the Number of Zeros for a Kind of Abel Integrals[J].Journal of SichuanNormal University,2019,(05):605-611.[doi:10.3969/j.issn.1001-8395.2019.05.006]
点击复制

一类Abel积分的零点个数估计()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
605-611
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
On the Number of Zeros for a Kind of Abel Integrals
文章编号:
1001-8395(2019)05-0605-07
作者:
王喜红
宁夏师范学院 数学与计算机科学学院, 宁夏 固原 756000
Author(s):
WANG Xihong
School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, Ningxia
关键词:
超椭圆Hamilton系统 幂零鞍点 Abel积分 ECT-系统
Keywords:
hyper-elliptic Hamiltonian system nilpotent saddle Abel integral ECT-system
分类号:
O175
DOI:
10.3969/j.issn.1001-8395.2019.05.006
文献标志码:
A
摘要:
研究Abel积分

的零点的个数问题,其中αi∈R,i=0,1,2,3,Γh={H(x,y)=h,h∈(-(1)/(20),0)}是闭曲线H(x,y)=(1)/(2)y2-(1)/(4)x4+(1)/(5)x5.当一个参数αi(i=0,1,2,3)为零时,得到J(h)在(-(1)/(20),0)上零点的精确个数.
Abstract:
In this paper, we study the number of zeros for Abel integrals
,
where αi∈R,i=0,1,2,3,Γh={H(x,y)=h,h∈(-(1)/(20),0)} are closed curves and H(x,y)=(1)/(2)y2-(1)/(4)x4+(1)/(5)x5.The exact number of zeros in(-(1)/(20),0)for J(h) is obtained when one of four parameters αi(i=0,1,2,3) vanishes.

参考文献/References:

[1] GAVRILOV L, ILIEV I.Complete hyperelliptic integrals of the first kind and their non-oscillation[J].Trans Am Math Soc,2004,356(3):1185-1207.
[2] WANG N, WANG J H, XIAO D M.The exact bounds on the number of zeros of complete hyperelliptic integrals of the first kind[J].J Diff Eqns,2013,254(2):323-341.
[3] GRAU M, MA(~overN)OSAS F, VILLADELPRAT J.A Chebyshev criterion for Abelian integrals[J].Trans Am Math Soc,2011,363(1):109-129.
[4] MA(~overN)OSAS F, VILLADELPRAT J.Bounding the number of zeros of certain Abeilian integrals[J].J Diff Eqns,2011,251(6):1656-1669.
[5] KARLIN S, STUDDEN W.Tchebycheff Systems:with Applications in Analysis and Statistics[M].New York:Interscience Publishers,1966.
[6] MARD(ˇoverS)(’overC)P.Chebyshev Systems and the Versal Unfolding of the Cusp of Order n[M].Paris:Hermann,1998.
[7] HAN M A, YANG J M, XIAO D M.Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle[J].International J Bifurcation & Chaos,2012,22(8):401-467.
[8] 朱道宇.一类三维分段线性系统的异宿轨的存在性[J].四川师范大学学报(自然科学版),2016,39(3):377-381.
[9] 万树园,王智勇.一类二阶Hamilton系统次调和解的存在性[J].四川师范大学学报(自然科学版),2017,40(2):172-176.
[10] 居加敏,王智勇.一类带阻尼项的次二次二阶Hamilton系统的周期解[J].四川师范大学学报(自然科学版),2015,38(3):329-332.
[11] 吴奎霖,刘倩.一类可逆系统周期轨道的周期函数的单调性判断[J].四川师范大学学报(自然科学版),2017,40(3):324-327.
[12] 黄勇,黄燕革.具有强迫项的有限时滞Lienard方程周期解的存在性[J].四川师范大学学报(自然科学版),2016,39(1):111-116.

备注/Memo

备注/Memo:
收稿日期:2017-11-29 接受日期:2018-01-04
基金项目:国家自然科学基金(11701306)和宁夏高等学校一流学科建设(教育学学科)资助项目(YLXKZD1730)
作者简介:王喜红(1965—),男,副教授,主要从事微分方程及其应用的研究,E-mail:xhwang6501@163.com
更新日期/Last Update: 2019-07-15