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In the main result of this paper, some sharp conditions are obtained for global attractivity in a scalar perturbed linear delay differential equation. The proof of the main theorem is based on a new estimate for the infinite integral of the absolute value of the fundamental solution of a linear delay differential equation. We also derive sufficient conditions for asymptotic stability of a system of linear delay differential equations. 相似文献
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Naotaka Imada 《Journal of Mathematical Analysis and Applications》1975,52(2):322-343
This paper discusses an asymptotic formula for solutions of a second-order linear differential equation. The asymptotic formula will enable us to provide information about the distribution of eigenvalues for the case of nonexistence of continuous spectrum in a singular Sturm-Liouville type boundary value problem. The result can be regarded as a partial generalization of those obtained by E. C. Titchmarsh and C. G. C. Pitts. 相似文献
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包立平 《高校应用数学学报(A辑)》2016,(3):307-315
文中讨论了一类奇摄动时滞抛物型偏微分方程的初边值问题,得到了其形式渐近展开,证明了奇摄动半线性时滞偏微分方程的极大值原理,从而得到了最大值估计及相应的Schuader估计.在此基础上,得到了柱状区域上解的存在唯一性和渐近解的一致有效性. 相似文献
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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
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We describe the bifurcation hypersurfaces for periodic solutions of a singularly perturbed linear differential difference equation in the space of the coefficients of the equation. For low dimension we show that the locus of stability of that equation approaches the locus of stability of a limit difference equation. 相似文献
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Yu A. Mitropol’skii 《Ukrainian Mathematical Journal》1998,50(1):66-82
We consider the application of the asymptotic method of nonlinear mechanics to the construction of the first and second approximations
of a solution of the Bremerton equation.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 58–71, January, 1998. 相似文献
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Yu. A. Mitropol'skii 《Ukrainian Mathematical Journal》1995,47(9):1378-1386
We consider an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation.Academician.Translated from Ukrainskii Matematicheskii Zhumal, Vol. 47, No. 9, pp. 1209–1216, September, 1995.This research is partially supported by the International Soros Foundation for Support of Education Program in Natural Sciences. 相似文献
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The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag 总被引:1,自引:0,他引:1
Hongjiong Tian 《Journal of Mathematical Analysis and Applications》2002,270(1):143-149
This paper is concerned with the exponential stability of singularly perturbed delay differential equations with a bounded (state-independent) lag. A generalized Halanay inequality is derived in Section 2, and in Section 3 a sufficient condition will be provided to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is exponentially stable uniformly for sufficiently small ε>0. This type of exponential asymptotic stability can obviously be applied to general delay differential equations with a bounded lag. 相似文献
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We treat the nonlinear Klein-Gordon (NKG) equation as the Sine-Gordon (SG) equation, perturbed by a higher order term. It
is proved that most small-amplitude finite-gap solutions of the SG equation, which satisfy either Dirichlet or Neumann boundary
conditions, persist in the NKG equation and jointly form partial central manifolds, which are “Lipschitz manifolds with holes”.
Our proof is based on an analysis of the finite-gap solutions of the boundary problems for SG equation by means of the Schottky
uniformization approach, and an application of an infinite-dimensional KAM-theory.
The first author was supported by the Alexander von Humbold Foundation and the Sonder-forschungsbereich 288. 相似文献
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Summary
The behavior of the solutions of a class of perturbed nonlinear second order differential equations is studied where the perturbation term may be unbounded in each of its arguments. Upper and lower bounds for solutions and a nonoscillation theorem are included in the results.Research supported by the Mississippi State University Biological and Physical Sciences Research Institute. 相似文献