Inertial manifolds for nonautomous infinite dimensional dynamical systems

In this paper, the long time behavior of nonautonomous infinite dimensional dynamical systems is discussed. Under the spectral gap condition, It is proved that there exist inertial manifolds for a class of nonautonomous evolution equations. Project supported by the National Natural Science Foundation of China     

固定位能的奇异Hamilton包含的守恒周期解

本文证明了奇异Hamilton包含—↑x∈ρ↓V（x）固定位能的守恒周期解的存在性。这里V:R^N\{0}→R是局部Lipschita连续函数，且在原点带有奇异性。     

The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)

In this paper the regularity of the Lagrangiansf(x, )=||^(x)(1< ₁(x)₂< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||^(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China.     

Lipschitz泛函的本质临界点

本文指出Ｂａｎａｃｈ空间中Ｃ^1－0（即局部Ｌｉｐｓｃｈｉｔｚ）泛函的Ｃｌａｒｋｅ－临界点一般不具有在Ｃ^1－0局部坐标变换下的不变性。据此提出了Ｃ^1－0泛函的本质临界点的概念，它能适应研究Ｃ^1－0流形上的Ｃ^1－0泛函的临界点的需要．还给出了有关本质临界点的几个结果。     

CONVERGENT FAMILIES OF APPROXIMATE INERTIAL MANIFOLDS FOR NONAUTONOMOUS EVOLUTION EQUATIONS

I.IntroduCtionAtpresent.autollomousinfillitedimensionaldynamicalsystemshavebeenthoroughlystLldicdilltllcory.andwidelyappliedinpracticel'-'1.Forthe11onautonomouscase,[5--91havesttldicd1ilocxistenceanddimensionestimateofattractorsofnonautonomouscase;[12].hasconsideredtileexislellceofinertialmanifolds.Theoretically,inertialmanifoldisaveryusefulInethodtodiscussthelongtimebehaviorofthesolutionstononautonomousinfinitedimcnsiollaldynamicalsystems.Butitcannotbeexpressedexplicitly.Soitisnotconvenient…     

Fredholm映射的集值紧摄动的拓扑度

Suppose that X is a paracompact oriented C` -Banach-Fredholm manifold, Ω is an open subset of X, E is a Banach space, f:Ω→E is a proper continuous map, f:Ω→E is an admissible (nonlinear) C′-Fredholm map of index zero,G:Ω→2^E is an upper semicontinuous compact set-valued map with compact convex values, p∈ E\(f-G)(?Ω). In this paper the degree deg(f-G,Ω,p) is defined.     

具无界值上半连续集值映射的拓扑度

设X和Y是Banach空间。用C(X)表示X中一切非空闭凸子产集所成之族。对于X中的点x与非空子集A和B,记,其中ε>0。 X×Y中的范数定义为。