变时滞非线性微分方程零解的渐近稳定性
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摘要
利用Banach不动点定理研究了变时滞非线性微分方程.在一定的条件下,通过构造适当的压缩映射,得到了方程在完备度量空间S_ψ上零解渐近稳定的新条件,即允许系数函数改变符号且不要求时滞有界,并通过算例证明了本文结论的有效性.
By using Banach fixed point theory, the nonlinear differential equation with variable delays is considered. Under certain conditions, by constrcutng appropriate contraction mappings, a new condition for asymptotic stability of zero solution of the equation on a complete metric space S_ψ is obtained. Allowing coefficient functions to change sign and do not require the boundedness of delays are given. An example is given to illustrate the validity of the conclusion in this paper.
By using Banach fixed point theory, the nonlinear differential equation with variable delays is considered. Under certain conditions, by constrcutng appropriate contraction mappings, a new condition for asymptotic stability of zero solution of the equation on a complete metric space S_ψ is obtained. Allowing coefficient functions to change sign and do not require the boundedness of delays are given. An example is given to illustrate the validity of the conclusion in this paper.
引文
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[4] ARDJOUNI A.Fixed points and stability in nonlinear neutral volterra intergo-differential equations with variable delays[J].Electronic Journal of Qualitative Theory of Differential Equations,2013,2013(28):1-13.
[5] ARDJOUNI A.Stability in totally nonlinear neutral differential equations with variable delay using fixed point[J].Proyecciones Journal of Mathematics,2015,34:25-44.
[6] MESMOULI M B.Periodic solutions and stability in a nonlinear neutral system of differential equations with infinite delay[J].Boletín de la Sociedad Matemática Mexicana,2018,24(1):239-255.
[7] 钟越.一类非线性Volterra方程零解的稳定性[J].数学物理学报,2015,35(5):878-883.
[8] GE F,KOU C.Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations[J].Applied Mathematics & Computation,2015,257:308-316.
[9] 姚洪兴.一类四阶时滞微分方程的渐进稳定性[J].江苏大学学报(自然科学版),2010,31(5):616-620.
[10] 黄明辉.多时滞的非线性微分方程的渐近稳定性[J].广东工业大学学报,2016,33(1):62-66.
[11] 黄明辉.带可积时滞的非线性中立型微分方程的h- 渐近稳定性[J].南阳师范学院学报,2017,38(9):5-11.
[2] ARDJOUNI A.Fixed points and stability in linear neutral differential equations with variable delays[J].Nonlinear Analysis,2011(74):2062-2070.
[3] JIN C H,LUO J W.Asymptotic stability of differential equations with several delays[J].Publ Math Debrecen,2011,78(1):89-102.
[4] ARDJOUNI A.Fixed points and stability in nonlinear neutral volterra intergo-differential equations with variable delays[J].Electronic Journal of Qualitative Theory of Differential Equations,2013,2013(28):1-13.
[5] ARDJOUNI A.Stability in totally nonlinear neutral differential equations with variable delay using fixed point[J].Proyecciones Journal of Mathematics,2015,34:25-44.
[6] MESMOULI M B.Periodic solutions and stability in a nonlinear neutral system of differential equations with infinite delay[J].Boletín de la Sociedad Matemática Mexicana,2018,24(1):239-255.
[7] 钟越.一类非线性Volterra方程零解的稳定性[J].数学物理学报,2015,35(5):878-883.
[8] GE F,KOU C.Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations[J].Applied Mathematics & Computation,2015,257:308-316.
[9] 姚洪兴.一类四阶时滞微分方程的渐进稳定性[J].江苏大学学报(自然科学版),2010,31(5):616-620.
[10] 黄明辉.多时滞的非线性微分方程的渐近稳定性[J].广东工业大学学报,2016,33(1):62-66.
[11] 黄明辉.带可积时滞的非线性中立型微分方程的h- 渐近稳定性[J].南阳师范学院学报,2017,38(9):5-11.