The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation

被引：0

作者：

Yanmei Sun ^{[1
,2
]}

Xiong Li ^{[1
]}

机构：

[1] School of Mathematical Sciences, Beijing Normal University

[2] School of Mathematics and Information Sciences, Weifang University

来源：

Science China Mathematics | 2018年 / 61卷 / 09期

基金：

中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;

关键词：

superlinear Duffing equations; blow-up; quasi-periodic solutions;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we construct a continuous positive periodic function p（t） such that the corresponding superlinear Duffing equation x′′+ a（x）;+p（t）x;= 0, n + 2≤2 m+1<2n+1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a（x） is an arbitrary positive smooth periodic function defined in the whole real axis.

引用

页码：51 / 64

页数：14

共 50 条

[1] The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation
Yanmei Sun
Xiong Li
[J]. Science China Mathematics, 2018, 61 : 1589 - 1602
[2] The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation
Sun, Yanmei
Li, Xiong
[J]. SCIENCE CHINA-MATHEMATICS, 2018, 61 (09) : 1589 - 1602
[3] The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems
Wang, Zhiguo
Wang, Yiqian
Lu, Hui
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (02) : 888 - 898
[4] Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation
YaqunPENG
XinliZHANG
DaxiongPIAO
[J]. Chinese Annals of Mathematics,Series B, 2021, 42 (01) : 85 - 104
[5] Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation
Yaqun Peng
Xinli Zhang
Daxiong Piao
[J]. Chinese Annals of Mathematics, Series B, 2021, 42 : 85 - 104
[6] Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation
Peng, Yaqun
Zhang, Xinli
Piao, Daxiong
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2021, 42 (01) : 85 - 104
[7] Periodic and quasi-periodic trajectories of the duffing equation
Nikitina, NV
Senchenkov, IK
[J]. INTERNATIONAL APPLIED MECHANICS, 1997, 33 (08) : 672 - 678
[8] Periodic and quasi-periodic trajectories of the Duffing equation
N. V. Nikitina
I. K. Senchenkov
[J]. International Applied Mechanics, 1997, 33 : 672 - 678
[9] On the Blow-Up of Solutions of a Periodic Shallow Water Equation
A. Constantin
[J]. Journal of Nonlinear Science, 2000, 10 : 391 - 399
[10] On the blow-up of solutions of a periodic shallow water equation
Constantin, A
[J]. JOURNAL OF NONLINEAR SCIENCE, 2000, 10 (03) : 391 - 399

← 1 2 3 4 5 →