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Pseudo Almost Automorphic Solutions for Non-autonomous Stochastic Differential Equations with exponential dichotomy

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Communications in Mathematical Research 2014年第2期30卷 139-156页

作者： Du Jin-shi Sun Kai Wang Yan Li Yong School of Mathematics Jilin University

In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.

关键词： pseudo almost automorphy exponential dichotomy non-autonomousstochastic differential equation

A GENERALIZATION OF A PROPOSITION ON exponential dichotomy

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Annals of Differential Equations 2000年第1期16卷 62-73页

作者：史金麟

It is well known that if x' = A(t)x admits an exponential dichotomy and f(t, x) is a bounded function and has a small Lipschitz constant, then system X' = A(x)x + f(t, x) has a unique bounded solution. In this paper, ... 详细信息

关键词： exponential dichotomy generalization

TOPOLOGICAL EQUIVALENCE FOR RECURRENT LINEAR SYSTEM WITH exponential dichotomy

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Annals of Differential Equations 2002年第1期18卷 65-71页

作者：汪宏喜

In this paper we discuss the recurrent linear system with exponential dichotomy, and prove that the system is topologically equivalent to the standard system where .

关键词： exponential dichotomy kinematical similarity recurrence topological equivalence

Almost Periodic Solutions by the Harmonic Balance Method

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 943-954页

作者： Ji-feng CHU Zuo-huan ZHENG Zhe ZHOU Department of Mathematics Shanghai Normal UniversityShanghai 200234China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China College of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China

We consider non-autonomous ordinary differential equations in two *** is the one-dimensional case that admits a condition of hyperbolicity,and the other one is the higher-dimensional case that admits an exponential *** differential equations of this kind,we give a rigorous treatment of the Harmonic Balance Method to look for almost periodic solutions.

关键词： almost periodic solution Harmonic balance method exponential dichotomy

Existence of local stable manifolds for some nondensely defined nonautonomous partial functional differential equations

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International Journal of Biomathematics 2019年第8期12卷 127-141页

作者： Amor Rebey Department of Mathematics College of Science and Human Studies at Hotat Sudair Majmaah University Al-Majmaah 11952Saudi Arabia ISMAIK Kairouan UniversityTunisia

In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function *** approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.

关键词： Evolution family mild solution exponential dichotomy admissibility of function spaces stable manifolds

Orbits Heteroclinic to Invariant Manifolds

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Acta Mathematica Sinica,English Series 1996年第4期12卷 372-373,375-378页

作者： Zhu Deming Department of Mathematics East China Normal University Shanghai, 200062 China Department of Mathematics East China Normal University Shanghai China

Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i... 详细信息

关键词： Invariant manifold exponential dichotomy Heteroclinic orbit Transversality

Problems in Homoclinic Bifurcation with Higher Dimensions

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Acta Mathematica Sinica,English Series 1998年第3期14卷 341-352页

作者： Zhu Deming Department of Mathematics, East China Normal University. Shanghai 200062. China Department of Mathematics East China Normal University 200062 Shanghai China

In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.

关键词： exponential dichotomy Local coordinates Homoclinic bifurcation Periodic orbit

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

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Journal of Partial Differential Equations 2017年第1期30卷 11-30页

作者： BAAZAOUI Riadh Department of Mathematics Faculty of Sciences of Tunis University Tunis EI-Manar1060 Tunis Tunisia.

In this work, a characterization of the doubly-weighted Bohr spectrum of an almost periodic function is given. We showed precisely that such a spectrum is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the existence of doubly-weighted pseudo-almost periodic solutions to some classes of non-autonomous partial evolution equations.

关键词： Evolution family exponential dichotomy acquistapace and Terreni conditions doublyweighted pseudo-almost periodic evolution equation nonautonomous equation.

Existence of μ-Pseudo Almost Periodic Solutions to Some Classes of Nonautonomous Partial Evolution Equations

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Journal of Partial Differential Equations 2018年第1期31卷 1-16页

作者： BAAZAOUI Riadh Department of Mathematics Faculty of Sciences of Tunis University TunisEI-Manar 1060 Tunis Tunisia.

In this paper, we use a recent works [5], where the authors provide a new ap-proach for pseudo almost periodic solution under the measure theory, under Acquistpace-Terreni conditions, we make extensive use of interpolation spaces and exponential di-chotomy techniques to obtain the existence of μ-pseudo almost periodic solutions tosome classes of nonautonomous partial evolution equations.

关键词： evolution family exponential dichotomy Acquistapace and Terreni conditions al-most periodic pseudo almost periodic under the light measure evolution equation nonau-tonomous equation.