共查询到20条相似文献,搜索用时 15 毫秒
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This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis. An analysis based on the energy method provides new results about the asymptotic stability of constant and periodic solutions. A complete analysis of the stability diagram is given in the linear homogeneous case. Under periodic forcing, existence of periodic solutions is discussed, involving a Diophantine condition on the period of the source. 相似文献
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U. an der Heiden 《Journal of Mathematical Analysis and Applications》1979,70(2):599-609
It is proved that the autonomous difference-differential equation
(0) has, for a broad class of functions f, a nonconstant periodic solution whenever the associated characteristic equation has a root with positive real part. 相似文献
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This paper studies the asymptotic behavior of solutions of the nonlinear delay differential equation with impulses
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Cemil Tunç 《Journal of the Egyptian Mathematical Society》2012,20(1):43-45
The aim of this paper is to establish an instability theorem for a certain sixth order nonlinear delay differential equation. The proof of the theorem is based on the use of Lyapunov–Krasovskii functional approach. By this work, we improve an instability result obtained in the literature for a certain sixth order nonlinear differential equation without delay to the instability of the zero solution of a certain sixth order nonlinear delay differential equation. 相似文献
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A differential equation approach to nonlinear programming 总被引:5,自引:0,他引:5
Hiroshi Yamashita 《Mathematical Programming》1980,18(1):155-168
A new method is presented for finding a local optimum of the equality constrained nonlinear programming problem. A nonlinear autonomous system is introduced as the base of the theory instead of usual approaches. The relation between critical points and local optima of the original optimization problem is proved. Asymptotic stability of the critical points is also proved. A numerical algorithm which is capable of finding local optima systematically at the quadratic rate of convergence is developed from a detailed analysis of the nature of trajectories and critical points. Some numerical results are given to show the efficiency of the method. 相似文献
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The paper is concerned with the higher order nonlinear neutral delay differential equation
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本文考虑一类非线性延迟微分方程-带有单调造血率的造血模型数值解的振动性.通过研究特征方程根的情况得到数值解振动的条件并且讨论了非振动的数值解的一些性质.为了更有力的说明我们的结果,最后给出了相应的算例. 相似文献
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The authors obtain results on the asymptotic behavior of the non-oscillatory solutions of a first order nonlinear neutral delay differential equation. A theorem giving sufficient conditions for all bounded solutions to be oscillatory is also proved. 相似文献
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A constructive method is presented for obtaining differential equation approximations to general functional delay differential equations. It is shown that the approximating differential equation systems can be used to determine the stability of the functional differential equations 相似文献
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Hans-Otto Walther 《Journal of Differential Equations》2008,244(8):1910-1945
We study a differential equation for delayed negative feedback which models a situation where the delay depends on the present state and becomes effective in the future. The main result is existence of a periodic solution in case the equilibrium is linearly unstable. The proof employs the ejective fixed point principle on a compact convex set K0⊂C([−h,0],R) of Lipschitz continuous functions and uses that the equation generates a smooth semiflow on an infinite-dimensional submanifold of the space C1([−h,0],R). 相似文献
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An elastic-plastic bar with simply connected cross section Q is clamped at the bottom and given a twist at the top. The stress function u, at a prescribed cross section, is then the solution of the variational inequality (0.1) is equal to the angle of the twist (after normalizing the units). Introducing the Lagrange multiplier λθ1, the unloading problem consists in solving the variational inequality (0.3) is the twisting angle for the unloaded bar; θ2 < θ1. Let (0.4) , and denote by the solutions of (0.1), (0.3), respectively, when K is replaced by . The following results are well known for the loading problem (0.1):(0.5) ; (0.6) the plastic set is connected to the boundary. In this paper we show that, in general, (0.7) ; (0.8) the plastic set is not connected to the boundary. That is, we construct domains Q for which (0.7) and (0.8) hold for a suitable choice of θ1, θ2. 相似文献
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George Karakostas 《Applicable analysis》2013,92(4):225-231
By using some facts from limiting equations theory we prove that the solution x(.;?), with continuous initial condition ?, of the neutral functional differential equation [x(t)-cx(t-r)]' =-F(x(t))+F(x(t-r)), t>0, where c ε [0,1), r≧0 and F is (not necessarily strictly) increasing. satisfies lim x(t;?) = &;, where &; is the unique root of the algebraic equation [math001] 相似文献
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B. S. Ogundare A. T. Ademola M. O. Ogundiran O. A. Adesina 《Annali dell'Universita di Ferrara》2017,63(2):333-351
This paper establishes explicit criteria in form of inequalities for all solutions to a class of second order nonlinear differential equations (with and without delay) to be bounded, ultimately bounded and globally asymptotically stable using Lyapunov second method. Obtained results are new and they complement existing results in the literature. Some examples are given to illustrate the main results. 相似文献
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We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given. 相似文献
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The abstract nonlinear boundary value problem , is treated. Existence and uniqueness results are obtained. 相似文献
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Genqiang Wang 《Journal of Mathematical Analysis and Applications》2004,298(1):298-307
Existence criteria are proved for the periodic solutions of a first order nonlinear differential equation with piecewise constant arguments. 相似文献