共查询到20条相似文献,搜索用时 15 毫秒
1.
The subject of the paper is to find existence conditions of weak solutions to multivalued stochastic differential equations with discontinuous coefficients. First we prove that a non-exploding solution exists when the drift coefficient b satisfies linear growth and the diffusion coefficient σ is uniformly elliptic. On this basis, we continue to obtain a solution (up to the explosion time) in the weak sense under certain local integrability, improving the result of Rozkosz and S?omiński. 相似文献
2.
Eduardo Liz 《Journal of Mathematical Analysis and Applications》2005,303(2):492-498
We derive some explicit sufficient conditions for the asymptotic stability of the zero solution in a general linear higher order difference equation, and compare our estimations with other related results in the literature. Our main result also applies to some nonlinear perturbations satisfying a kind of sublinearity condition. 相似文献
3.
We give Lyapunov exponents of solutions to linear differential equations of the form x′=Ax+f(t), where A is a complex matrix and f(t) is a τ-periodic continuous function. Notice that f(t) is not “small” as t→∞. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1-19] of solutions to the above equation. 相似文献
4.
Zhifei Zhang 《Journal of Mathematical Analysis and Applications》2010,363(2):549-558
We discuss the existence of periodic solutions to the wave equation with variable coefficients utt−div(A(x)∇u)+ρ(x,ut)=f(x,t) with Dirichlet boundary condition. Here ρ(x,v) is a function like ρ(x,v)=a(x)g(v) with g′(v)?0 where a(x) is nonnegative, being positive only in a neighborhood of a part of the domain. 相似文献
5.
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
6.
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients have the
formt
-α
a(t), α > 0 wherea(t) is a trigonometric polynomial with an arbitrary set of frequencies. The asymptotic behavior of the solutions of this system
ast → ∞ is studied. We construct an invertible (for sufficiently larget) change of variables that takes the original system to a system not containing oscillatory coefficients in its principal
part. The study of the asymptotic behavior of the solutions of the transformed system is a simpler problem. As an example,
the following equation is considered:
, where λ andα, 0 <α ≤ 1, are real numbers.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 658–666, November, 1998. 相似文献
7.
Let denote the set of continuous n×n matrices on an interval . We say that is a nontrivial k-involution if where ζ=e-2πi/k, d0+d1++dk-1=n, and with . We say that is R-symmetric if R(t)A(t)R-1(t)=A(t), , and we show that if A is R-symmetric then solving x′=A(t)x or x′=A(t)x+f(t) reduces to solving k independent dℓ×dℓ systems, 0ℓk-1. We consider the asymptotic behavior of the solutions in the case where . Finally, we sketch analogous results for linear systems of difference equations. 相似文献
8.
Pham Huu Anh Ngoc Hieu Trinh Le Trung Hieu Nguyen Dinh Huy 《Mathematische Nachrichten》2019,292(4):859-870
General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay. 相似文献
9.
I.- G. E. Kordonis Ch.G. Philos 《Journal of Difference Equations and Applications》2013,19(3):219-233
A class of linear autonomous neutral delay difference equations is considered, and some new results on the asymptotic behavior and the stability are given, via a positive root of the correspondng characteristic equation. 相似文献
10.
Abdullah Alotaibi 《Journal of Mathematical Analysis and Applications》2010,367(2):451-460
The first result of the paper concerns the effect of perturbation of the entire coefficients of certain linear differential equations on the oscillation of the solutions. Subsequent results involve the separation of the zeros of a Bank-Laine function. 相似文献
11.
In this paper we investigate the stability of linear singular systems of difference equations with variable coefficients by the projector-based approach. We study the preservation of uniform/exponential stability when the system coefficients are subject to allowable perturbations. A Bohl–Perron type theorem is obtained which provides a necessary and sufficient condition for the boundedness of solutions of nonhomogenous systems. The notion of Bohl exponent is introduced and we characterize the relation between the exponential stability and the Bohl exponent. Finally, robustness of the Bohl exponent with respect to allowable perturbations is investigated. 相似文献
12.
Under study are the systems of quasilinear delay differential equations with periodic coefficients of linear terms. We establish sufficient conditions for the asymptotic stability of the zero solution, obtain estimates for solutions which characterize the decay rate at infinity, and find the attractor of the zero solution. Similar results are obtained for systems with parameters. 相似文献
13.
Asymptotic solutions and error estimates for linear systems of difference and differential equations
Classical results concerning the asymptotic behavior solutions of systems of linear differential or difference equations lead to formulas containing factors that are asymptotically constant, i.e., k+o(1) as t tends to infinity. Here we are interested in more precise information about the o(1) terms, specifically how they depend precisely on certain perturbation terms in the equation. Results along these lines were given by Gel'fond and Kubenskaya for scalar difference equations and we will both extend and generalize one of them as well as provide some corresponding results for differential equations. 相似文献
14.
In this paper we investigate the iterated order, iterated type and iterated convergence exponent of zeros of meromorphic solutions of the equations
15.
Some new results on the behavior of the solutions to periodic linear delay differential equations as well as to periodic linear delay difference equations are given. These results are obtained by the use of two distinct roots of the corresponding (so called) characteristic equation. 相似文献
16.
A.D. Myshkis 《Journal of Difference Equations and Applications》2013,19(5-6):571-576
The concept of a linear operator with constant coefficients is introduced and investigated, for which the corresponding first boundary problem is uniquely solvable ( or stable uniquely sovable) for any finite net set. 相似文献
17.
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19.
In this paper, we give the definition of iterated order to classify functions of fast growth in the unit disc, and investigate the growth of solutions of linear differential equations with analytic coefficients of iterated order in the unit disc. We obtain several results concerning the iterated order of solutions. 相似文献
20.
Standard results on asymptotic integration of systems of linear differential equations give sufficient conditions which imply that a system is strongly asymptotically equivalent to its principal diagonal part. These involve certain dichotomy conditions on the diagonal part as well as growth conditions on the off-diagonal perturbation terms. Here, we study perturbations with a triangularly-induced structure and see that growth conditions can be substantially weakened. In addition, we give results for not necessarily triangular perturbations which in some sense “interpolate” between the classical theorems of Levinson and Hartman-Wintner. Some analogous results for systems of linear difference equations are also given. 相似文献