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Stefan Siegmund 《Journal of Dynamics and Differential Equations》2002,14(1):243-258
For nonautonomous linear differential equations x=A(t) x with locally integrable A: RR
N×N
the so-called dichotomy spectrum is investigated in this paper. As the closely related dichotomy spectrum for skew product flows with compact base (Sacker–Sell spectrum) our dichotomy spectrum for nonautonomous differential equations consists of at most N closed intervals, which in contrast to the Sacker–Sell spectrum may be unbounded. In the constant coefficients case these intervals reduce to the real parts of the eigenvalues of A. In any case the spectral intervals are associated with spectral manifolds comprising solutions with a common exponential growth rate. The main result of this paper is a spectral theorem which describes all possible forms of the dichotomy spectrum. 相似文献
5.
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions. 相似文献
6.
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 相似文献
7.
Based upon the conservation of average energy a theorem about the periodic solutions of strongly nonlinear nonautomous systems with multi-degree-of freedom is proved. This theorem can not only decide the existence and stability of the periodic solutions, but at the same time can also give their first-order and second-order approximate expressions. 相似文献
8.
Peng Yang JinRong Wang Michal Fe
kan 《Mathematical Methods in the Applied Sciences》2019,42(10):3700-3720
In this paper, we study a new class of periodic nonautonomous differential equations with periodic noninstantaneous impulsive effects. A concept of noninstantaneous impulsive Cauchy matrix is introduced, and some basic properties are considered. We give the representation of solutions to the homogeneous problem and nonhomogeneous problem by using noninstantaneous impulsive Cauchy matrix, and the variation of constants method, adjoint systems, and periodicity of solutions is verified under standard periodicity conditions. Further, we show the existence and uniqueness of solutions of semilinear problem and establish existence result for periodic solutions via Brouwer fixed point theorem and uniqueness and global asymptotic stability via Banach fixed point theorem. 相似文献
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Received September 24, 1998; accepted August 9, 1999 相似文献
10.
非自治Lotka—Volterra竞争系统 总被引:2,自引:0,他引:2
讨论了一般n个种群的非自治Lotka-Volterra竞争系统,给出了系统的正解灭绝的一个充分条件。文献「1,2」中的主要结果被很好地推广。 相似文献