STABLE AND UNSTABLE MANIFOLDS FORNONLINEAR PARTIAL NEUTRAL FUNCTIONALDIFFERENTIAL EQUATIONS

RACHID BENKHALTI; KHALIL EZZINBI; SAMIR FATAJOU

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STABLE AND UNSTABLE MANIFOLDS FORNONLINEAR PARTIAL NEUTRAL FUNCTIONALDIFFERENTIAL EQUATIONS

机译：非线性部分中性泛函微分方程的稳定和不稳定流形

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The aim of this work is to investigate the asymptotic behav-ior of solutions near hyperbolic equilibria for nonlinear partial neutralfunctional differential equations. We suppose that the linear part Asatisfies the Hille-Yosida condition on a Banach space and is not nec-essarily densely defined; the delayed part is assumed to be Lipschitz.We show the existence of stable and unstable manifolds near hyperbolicequilibria when the neutral operator is stable and the semigroup gener-ated by the part of A in D(A) is compact. Local stable and unstablemanifolds are also obtained when the undelayed part is a C~1function ina neighborhood of the equilibria.

机译：这项工作的目的是研究非线性中立型泛函微分方程在双曲平衡附近解的渐近行为。我们假设线性部分满足Banach空间上的Hille-Yosida条件，并且没有必要密集地定义;当中立算子稳定且由D（A）中A生成的半群为紧时，表明双曲均衡附近存在稳定流形和不稳定流形。当未延迟部分是平衡区附近的C〜1函数时，也会获得局部稳定和不稳定流形。

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来源
《Differential and integral equations》 |2010年第8期|共22页
作者
RACHID BENKHALTI; KHALIL EZZINBI; SAMIR FATAJOU;
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原文格式 PDF
正文语种 eng
中图分类微分方程、积分方程;
关键词
solutions; existence; equilibria;

机译：解;存在性;均衡;

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1. 泛函微分方程的不稳定性定理与稳定的充要条件 [J] . 冯祐和数学年刊：B辑英文版 . 1993,第002期
2. STABLE AND UNSTABLE MANIFOLDS FORNONLINEAR PARTIAL NEUTRAL FUNCTIONALDIFFERENTIAL EQUATIONS [J] . RACHID BENKHALTI, KHALIL EZZINBI, SAMIR FATAJOU Differential and integral equations . 2010,第7a8期

机译：非线性部分中性泛函微分方程的稳定和不稳定流形
3. STABLE MANIFOLDS FOR SOME PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NON-DENSE DOMAIN [J] . Jendoubi Chiraz The Journal of integral equations and applications . 2019,第3期

机译：具有非致密结构域的一些部分中性功能微分方程的稳定歧管
4. Admissibly Stable Manifolds for a Class of Partial Neutral Functional Differential Equations on a Half-line [J] . Thieu Huy Nguyen, Xuan Yen Trinh Taiwanese journal of mathematics . 2019,第4期

机译：在半线上的一类部分中性功能微分方程提供稳定的歧管
5. Oscillation of Unstable Second Order Neutral Differential Equations with Positive and Negative Coefficients [C] . XU Ji-jun International Conference on Frontiers of Energy, Materials and Information Engineering . 2014

机译：具有正负系数的不稳定二阶中性微分方程的振动
6. A FUNDAMENTAL EQUATION REPRESENTING WATER IN STABLE, METASTABLE AND UNSTABLE STATES [D] . KARIMI, AMIR. 1982

机译：处于稳定，亚稳态和不稳定状态的基本方程组
7. An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics [O] . Chunjiang Fu, Yasuyuki Suzuki, Ken Kiyono, 2014

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8. The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations II: Existence of stable and unstable manifolds [O] . Mohammed, Salah-Eldin A., Zhang, Tusheng, Zhao, Huaizhong 2005

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STABLE AND UNSTABLE MANIFOLDS FORNONLINEAR PARTIAL NEUTRAL FUNCTIONALDIFFERENTIAL EQUATIONS

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