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991.
邓冠铁 《数学物理学报(A辑)》2007,27(3):414-419
该文对一类复指数多项式组成的线性空间$M(\Lambda )$ 在Banach 空间 Hα中的不完备性给出了充分必要条件, 其中 Hα为在半带形 Iα={z=x+iy: x≥ 0, |y|≤α} (α > 0 )中连续, 在Iα的内部解析且当 x→∞时, f(x+ iy)在Iα中关于 y 一致地 趋向 0 的函数 f(x+ iy)全体, 其范数为上确界范数. 同时指出, 如果$M(\Lambda )$ 在 Hα中不完备, 则它的闭包cl$(M(\Lambda ))$中所有的函数都可以延拓为由Dirichlet级数表示的解析函数. 相似文献
992.
This paper is concerned with the asymptotic behavior of solutions of the critical generalized Korteweg-de Vries equation in a bounded interval with a localized damping term. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay of the energy is reduced to prove the unique continuation property of weak solutions. A locally uniform stabilization result is derived.
993.
We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with
non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D
2(D
2–p
2), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives
by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We
show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to
achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth
enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C
1, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C
2 tension exponential splines.
相似文献
994.
We construct topological conjugacies between linear and nonlinear evolution operators that admit either a nonuniform exponential contraction or a nonuniform exponential dichotomy. We consider evolution operators defined by nonautonomous differential equations x′=A(t)x+f(t,x) in a Banach space. The conjugacies are obtained by first considering sufficiently small linear and nonlinear perturbations of linear equations x′=A(t)x. In the case of linear perturbations, we construct in a more or less explicit manner topological conjugacies between the two linear flows. In the case of nonlinear perturbations, we obtain a version of the Grobman-Hartman theorem for nonuniformly hyperbolic dynamics. Furthermore, all the conjugacies that we construct are locally Hölder continuous provided that the vectors fields are of class C1. As a byproduct of our approach, we give conditions for the robustness of strong nonuniform exponential behavior, in the sense that under sufficiently small perturbations the structure determined by the stable and unstable bundles persists up to small variations. We also show that the constants determining the nonuniform exponential contraction or nonuniform exponential dichotomy vary continuously with the perturbation. All the results are obtained in Banach spaces. 相似文献
995.
In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result. 相似文献
996.
拟线性Burgers方程在空间离散后转化成常微分方程,再用指数积分方法求解.数值结果表明指数积分法有显式稳定性,有相应Runge-Kutta方法相同的精度. 相似文献
997.
Yuliang Han 《Journal of Mathematical Analysis and Applications》2007,336(2):962-974
In this paper almost periodic random sequence in probability is defined and investigated. It is also applied to random difference equations by means of exponential dichotomy. The existence of such kind of solutions of random difference equations is discussed. 相似文献
998.
本文利用指数型二分性理论讨论了一般高维概周期系统的概周期解的存在性和唯一性,所得结果推广了Ezeilo的一个概周期解的存在性定理 相似文献
999.
C~m空间中非线性Lipschitz连续算子的定量性质 总被引:4,自引:0,他引:4
在有限维复Banach空间Cm中,全体Lipschitz连续算子构成一赋半范的非线性算子空间L(Cm).本文研究L(Cm)中非线性算子的定量性质,包括:L(Cm)中可逆算子到不可逆算子集合的逼近距离、L(Cm)中算子乘幂压缩的逆问题以及L(Cm)中算子的数值值域与谱集的联系,文中所得结果推广了线性算子理论中许多著名结论. 相似文献
1000.
具有强迫项Lienard类型方程周期解及概周期解的存在性 总被引:4,自引:1,他引:4
本文利用指数型二分性理论,给出具有强迫项的Lienard类型方程周期解及概周期解存在的充分条件,这些条件是由FinkA.M.,林发兴在文[1,2]对Lienard方程关于同样问题所获结果的自然扩展与推广 相似文献