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991.
992.
Yong-Kui Chang Zhi-Han Zhao Juan J. Nieto 《Numerical Functional Analysis & Optimization》2013,34(12):1219-1238
This article is mainly concerned with the existence and uniqueness of almost periodic and pseudo almost periodic mild solutions to a class of partial differential equations in Banach spaces. Under some reasonable assumptions, the main results are proved in α-norm. Our results cover the cases that the functions F 1; F 2 take values in different spaces such as X, X α, and X ß, where α ≤ β ∈ (0; 1). 相似文献
993.
In this paper, a new kind of iteration technique for solving nonlinear ordinary differential equations is described and used to give approximate periodic solutions for some well-known nonlinear problems. The most interesting features of the proposed methods are its extreme simplicity and concise forms of iteration formula for a wide range of nonlinear problems. 相似文献
994.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(6):1061-1093
In this work, we establish a new concept of pseudo almost periodic processes in p-th mean sense using the measure theory. We use the μ-ergodic process to define the spaces of μ-pseudo almost periodic process in the p-th mean sense. We establish many interesting results on the functional space of such processes like completeness and composition theorems. The main objective of this paper is to use those results and some stochastic analysis approaches to study the existence, the uniqueness and the global attractiveness for a μ-pseudo almost periodic mild solution to a class of abstract stochastic evolution equations driven by fractional Brownian motion. We provide an example to illustrate our results. 相似文献
995.
本文研究了高阶线性微分方程$$f^{(k)}(z)+A_{k-2}(z)f^{(k-2)}(z)+\cdots+A_0(z)f(z)=0,\eqno(*)$$解的线性相关性,其中$A_j(z)(j=0,2,\ldots,k-2)$是常数, $A_1$为非常数的的整周期函数,周期为$2\pi i$,且是$e^z$的有理函数.在一定条件下,我们给出了方程(*)解的表示. 相似文献
996.
In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form
997.
The paper is concerned with the existence of almost periodic solutions to the so-called semilinear thermoelastic plate systems. For that, the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations
(*) 相似文献
998.
In this paper, we prove the invariance of Stepanov-like pseudo-almost periodic functions under bounded linear operators. Furthermore, we obtain existence and uniqueness theorems of pseudo-almost periodic mild solutions to evolution equations u′(t)=A(t)u(t)+h(t) and on , assuming that A(t) satisfy “Acquistapace–Terreni” conditions, that the evolution family generated by A(t) has exponential dichotomy, that R(λ0,A()) is almost periodic, that B,C(t,s)t≥s are bounded linear operators, that f is Lipschitz with respect to the second argument uniformly in the first argument and that h, f, F are Stepanov-like pseudo-almost periodic for p>1 and continuous. To illustrate our abstract result, a concrete example is given. 相似文献
999.
We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup
H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx
−1, onto the subset of idempotents E(S) of S, is continuous.
相似文献
1000.
Guillaume James Pascal Noble Yannick Sire 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(4):1237-1264
We study relative periodic orbits (i.e. time-periodic orbits in a frame rotating at constant velocity) in a class of triatomic Euclidean-invariant (planar) Hamiltonian systems. The system consists of two identical heavy atoms and a light one, and the atomic mass ratio is treated as a continuation parameter. Under some nondegeneracy conditions, we show that a given family of relative periodic orbits existing at infinite mass ratio (and parametrized by phase, rotational degree of freedom and period) persists for sufficiently large mass ratio and for nearby angular velocities (this result is valid for small angular velocities). The proof is based on a method initially introduced by Sepulchre and MacKay [J.-A. Sepulchre, R.S. MacKay, Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity 10 (1997) 679–713] and further developed by Muñoz-Almaraz et al. [F.J. Muñoz-Almaraz, et al., Continuation of periodic orbits in conservative and Hamiltonian systems, Physica D 181 (2003) 1–38] for the continuation of normal periodic orbits in Hamiltonian systems. Our results provide several types of relative periodic orbits, which extend from small amplitude relative normal modes [J.-P. Ortega, Relative normal modes for nonlinear Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 665–704] up to large amplitude solutions which are not restrained to a small neighborhood of a stable relative equilibrium. In particular, we show the existence of large amplitude motions of inversion, where the light atom periodically crosses the segment between heavy atoms. This analysis is completed by numerical results on the stability and bifurcations of some inversion orbits as their angular velocity is varied. 相似文献