Periodic Solution and Global Stability of a Kind of Nonlinear Differential Equation

Chinese Quarterly Journal of Mathematics ›› 2001, Vol. 16 ›› Issue (1): 79-87.

Periodic Solution and Global Stability of a Kind of Nonlinear Differential Equation

北京建筑工程学院北京100044,西安交通大学陕西西安710049,北京林业大学北京100083

Received:1998-09-08 Online:2001-03-30 Published:2024-06-25
About author:SONG Guo-hua（1955－）,male,native of Ji’an,Jilin,a professor of Beijing Architectural and Civil Engineering Institute,Ph．D．,engages in differenfial equation．

Abstract

Abstract: 本文研究下面一类非线性微分方程... .如果条件m₂ x₂ (k₁δ+s₀δ-Qλ₂-x₂)² >m₁ δk₁ (k₂ +Q² λ₂ )²成立时 ,系统在Ω内存在周期解 ;如果条件m₂x₂(k₁δ +s₀δ -Qλ² -x₂ )² <m₁ δk₁ (k₂ -Q² λ₂ )²成立时 ,系统的轨线在内关于奇点 (s ,x₁ ,x₂)是全局稳定的 .

Key words: 非线性微分方程, 周期解, 稳定性, ,

CLC Number:

O175.13

SONG Guo-hua, LI Xiu-qin, DOU Jia-wei, HE Qing-tang. Periodic Solution and Global Stability of a Kind of Nonlinear Differential Equation[J]. Chinese Quarterly Journal of Mathematics, 2001, 16(1): 79-87.

[1]	JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei. Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 111-127.
[2]	PANG Ru-yi, CHEN Qiao-ling. Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 128-143.
[3]	XIN Xin, XIE Bo-yi, LIU Ke-ke. Sure Independence Screening via Semiparameteric Copula Learning [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 144-160.
[4]	XI Wei-ge, XU Tao. Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 161-170.
[5]	FANG Han-bing, XU Bin, YANG Bai-rui. The Gauss-Bonnet Formula of a Conical Metric on a Compact Riemann Surface [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 180-184.
[6]	XU Yun-long, ZHONG Yu-min. On Minkowski Constants of Bouw-M¨oller Surfaces [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 185-199.
[7]	GUAN Daniel, LIANG Meng-xiang. Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br# [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(2): 200-220.
[8]	TANG Zhong-hua, FANG Shao-mei. Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 18-30.
[9]	HONG Yong, ZHAO Qian. Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 59-67.
[10]	PAN Jia-hui, FANG Shao-mei. Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 360-369.
[11]	WANG Xiao-yuan, LIU Ya-juan. Subordination and Superordination Results for a Certain of Integral Operator Involving Generalized Mittag-Leffler Functions [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 379-391.
[12]	SUN Xiao-lei. Competitive Equilibrium of Central Bank Digital Currency and Private Cryptocurrency: A Perspective of Regulatory [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 415-423.
[13]	YANG Yi-song. Some Applications of Surface Curvatures in Theoretical Physics [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 221-253.
[14]	GUAN Daniel. Some Applications of Group Actions in Complex Geometry [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 254-275.
[15]	QIN Yu-ming, CHEN Jia-le, JIANG Hui-te. A New Existence Theorem for Global Attractors and its Application to a Non-Classical Diffusion Equation [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 276-289.

Periodic Solution and Global Stability of a Kind of Nonlinear Differential Equation

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments