共查询到20条相似文献,搜索用时 15 毫秒
1.
A. I. Gerko 《Mathematical Notes》2000,67(6):707-717
In the paper methods from the theory of extensions of dynamical systems are used to studyβ-differential equations whose solutions possess the uniqueness property and depend continuously on the initial data and on
the right-hand side of the equation. The Zhikov-Bronshtein theorems concerning asymptotically almost periodic solutions of
ordinary differential equations are extended toβ-differential equations (in particular, to total differential equations). Along with asymptotic almost periodicity, we also
consider asymptotic recurrence, weak asymptotic distality, and asymptotic distality. To the equations we associate dynamical
systems generated by the space of the right-hand sides and the spaces of the solutions and of the initial data of solutions
of the equation. Generally, the phase semigroups of the dynamical systems are not locally compact.
Translated fromMatermaticheskie Zametki, Vol. 67, No. 6, pp. 837–851, June, 2000. 相似文献
2.
D. N. Cheban 《Mathematical Notes》1998,63(1):102-111
In this paper we study the connection between the uniform asymptotic stability and the power-law or exponential asymptotics
of the solutions of infinite-dimensional systems (differential equations in Banach spaces, functional differential equations,
and completely solvable multidimensional differential equations).
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 115–126, January, 1998. 相似文献
3.
V. B. Levenshtam 《Journal of Mathematical Sciences》2009,163(1):89-110
A complete asymptotic expansion is constructed for solutions of the Cauchy problem for nth order linear ordinary differential
equations with rapidly oscillating coefficients, some of which may be proportional to ω
n/2, where ω is oscillation frequency. A similar problem is solved for a class of systems of n linear first-order ordinary differential
equations with coefficients of the same type. Attention is also given to some classes of first-order nonlinear equations with
rapidly oscillating terms proportional to powers ω
d
. For such equations with d ∈ (1/2, 1], conditions are found that allow for the construction (and strict justification) of the leading asymptotic term
and, in some cases, a complete asymptotic expansion of the solution of the Cauchy problem. 相似文献
4.
For a class of retarded linear differential equations with solutions of exponential form, it is shown that L
p
-perturbations leave the solutions of the same form. As a particular example, the asymptotic integration of a class of differential
equations is obtained. 相似文献
5.
For a class of retarded linear differential equations with solutions of exponential form, it is shown that L
p
-perturbations leave the solutions of the same form. As a particular example, the asymptotic integration of a class of differential
equations is obtained.
(Received 10 August 1998) 相似文献
6.
K. T. Joseph 《Proceedings Mathematical Sciences》2005,115(4):509-517
In this paper we study the asymptotic behaviour of solutions of a system ofN partial differential equations. WhenN = 1 the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous case
and show a new feature in the asymptotic behaviour. 相似文献
7.
Shoufu LI 《Frontiers of Mathematics in China》2009,4(1):23-48
In this review, we present the recent work of the author in comparison with various related results obtained by other authors
in literature. We first recall the stability, contractivity and asymptotic stability results of the true solution to nonlinear
stiff Volterra functional differential equations (VFDEs), then a series of stability, contractivity, asymptotic stability
and B-convergence results of Runge-Kutta methods for VFDEs is presented in detail. This work provides a unified theoretical foundation
for the theoretical and numerical analysis of nonlinear stiff problems in delay differential equations (DDEs), integro-differential
equations (IDEs), delayintegro-differential equations (DIDEs) and VFDEs of other type which appear in practice.
相似文献
8.
For a large class of partial differential equations on exterior domains or on ?N we show that any solution tending to a limit from one side as x goes to infinity satisfies the property of “asymptotic spherical symmetry”. The main examples are semilinear elliptic equations, quasilinear degenerate elliptic equations, and first-order Hamilton-Jacobi equations. 相似文献
9.
Liping Wen Yuexin Yu Shoufu Li 《Journal of Computational and Applied Mathematics》2009,230(2):351-359
This paper is concerned with the stability and asymptotic stability of θ-methods for the initial value problems of nonlinear stiff Volterra functional differential equations in Banach spaces. A series of new stability and asymptotic stability results of θ-methods are obtained. 相似文献
10.
《随机分析与应用》2013,31(5):715-751
In this paper we investigate several properties of the stabilizing solution of a class of systems of Riccati type differential equations with indefinite sign associated to controlled systems described by differential equations with Markovian jumping. We show that the existence of a bounded on R + and stabilizing solution for this class of systems of Riccati type differential equations is equivalent to the solvability of a control-theoretic problem, namely disturbance attenuation problem. If the coefficients of the considered system are theta;-periodic functions then the stabilizing solution is also theta;-periodic and if the coefficients are asymptotic almost periodic functions, then the stabilizing solution is also asymptotic almost periodic and its almost periodic component is a stabilizing solution for a system of Riccati type differential equations defined on the whole real axis. One proves also that the existence of a stabilizing and bounded on R + solution of a system of Riccati differential equations with indefinite sign is equivalent to the existence of a solution to a corresponding system of matrix inequalities. Finally, a minimality property of the stabilizing solution is derived. 相似文献
11.
We investigate smoothness properties of the roots of algebraic equations with almost constant coefficients and construct a transformation, which may be efficiently used for the investigation of the asymptotic behavior of a fundamental family of solutions of a broad class of nonautonomous linear differential equations of the nth order. 相似文献
12.
Extremal solutions to a system of n nonlinear differential equations and regularly varying functions
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The strongly increasing and strongly decreasing solutions to a system of n nonlinear first order equations are here studied, under the assumption that both the coefficients and the nonlinearities are regularly varying functions. We establish conditions under which such solutions exist and are (all) regularly varying functions, we derive their index of regular variation and establish asymptotic representations. Several applications of the main results are given, involving n‐th order nonlinear differential equations, equations with a generalized ?‐Laplacian, and nonlinear partial differential systems. 相似文献
13.
A. A. Él’nazarov 《Ukrainian Mathematical Journal》1998,50(3):507-513
By using the method of asymptotic expansion of anm-parameter family of solutions, we obtain the asymptotic expansion of solutions of a quasilinear system of differential equations.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50,
No. 3, pp. 445–450, March, 1998. 相似文献
14.
Carlos Lizama 《Applicable analysis》2013,92(8):1731-1754
We propose a unified functional analytic approach to derive a variation of constants formula for a wide class of fractional differential equations using results on (a,?k)-regularized families of bounded and linear operators, which covers as particular cases the theories of C 0-semigroups and cosine families. Using this approach we study the existence of mild solutions to fractional differential equation with nonlocal conditions. We also investigate the asymptotic behaviour of mild solutions to abstract composite fractional relaxation equations. We include in our analysis the Basset and Bagley–Torvik equations. 相似文献
15.
We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform
meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs
is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE. 相似文献
16.
A. Zafer 《Applicable analysis》2013,92(9):899-908
The asymptotic equivalence of systems of difference equations of linear and quasilinear type is investigated. The first result on the asymptotic equivalence of linear systems is a discrete analog of an improved version of the Levinson's well-known theorem on asymptotic equivalence of linear differential equations, while the second one providing conditions for asymptotic equivalence of linear and quasilinear systems is related to that of Yakubovich in differential equations case. 相似文献
17.
J. Robert Buchanan 《Natural Resource Modeling》1998,11(1):5-19
Averaging methods are used to compare solutions of two-dimensional systems of ordinary differential equations with constant or periodic forcing. The asymptotic separation of solutions of the periodically forced equations from the solutions of the constantly forced equations is proportional to the L1 norm of the periodic forcing terms. This result is applied to population models of Kolmogorov-type with climax fitness functions where forcing represents stocking or harvesting of a population. The asymptotic behavior of such systems may be controlled, to some extent, by varying the period and/or amplitude of the forcing functions. 相似文献
18.
For a system of differential equations with small parameter at a part of derivatives, a linear deviation of the argument,
and a turning point, we obtained conditions, under which its solutions are solutions of a system of differential equations
with small parameter at a part of derivatives such that its matrices possess the asymptotic expansions at |ε| ≤ ε0 with the coefficients holomorphic at |x| ≤ x
0
. The existence and the infinite differentiability of a solution of the system of differential equations with small parameter
at a part of derivatives and with a linear deviation of the argument in the presence of a turning point are proved. 相似文献
19.
Fathalla A. Rihan 《Numerical Methods for Partial Differential Equations》2010,26(6):1556-1571
This article is concerned with ?‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
20.
E. P. Belan 《Journal of Mathematical Sciences》1994,70(5):1956-1959
A method of constructing of an asymptotic expansion of quasiperiodic solutions of systems of nonlinear ordinary differential equations of second order is given. The nonresonance and resonance cases are considered.Translated from Dinamicheskie Sistemy, No. 9, pp. 10–15, 1990. 相似文献