共查询到19条相似文献,搜索用时 94 毫秒
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在研究滞后型泛函微分方程解的稳定性过程中,Razumikhin 型定理颇被人们重视.文〔1〕指出:“它的优点在于(dv)/(dt)可直接与方程右端算子发生关系,适合具体应用问题”,本文改进了文〔2〕中的 Razumikhin 型定理,可适用于一般的滞后型泛函微分方程(RFDE),引进了强等度渐近稳定的概念,给出了一类特殊滞后系统的解具有此种稳定性的充要条件及一致渐近稳定的充分条件. 相似文献
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一类泛函微分方程周期解的存在性与应用 总被引:6,自引:1,他引:5
本文给出了一类滞后型泛函微分方程有一个周期解的四个充分性定理,其结果明显地优于著名的Yoshizawa周期解定理,最后给出了应用实例。 相似文献
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无限时滞泛函微分方程周期解的存在性 总被引:3,自引:0,他引:3
王克 《数学年刊A辑(中文版)》1987,(4)
J.K.Hale和J.Kato关于具无限时滞的滞后型泛函微分方程提出了很好的相空间理论,以这个理论为基础,本文把T.Yoshizawa的一个著名的关于有限时滞方程周期解的存在性定理推广到无限时滞的情况。 相似文献
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§1.引言对超前型泛函微分方涅,文献[1]~[6]在x(s)=ξ的初始条件下研究了它在[s, ∞)上为有界的解,本文沿用这种初值问题的提法,探讨具有非线性扰动项的超前型泛函微分方程 相似文献
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曹彩霞 《数学的实践与认识》2008,38(12):214-215
研究了一类非线性滞后型泛函微分方程周期解的存在性问题.通过Ляпунов方法给出了存在周期解的充分条件和时滞范围的简明表达式,并推广了若干已知结果. 相似文献
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本文研究线性中立型Volterra积分微分方程的解的振动性,应用Gershgorin定理,得到了方程所有有界解振动的充分条件。 相似文献
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A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions. 相似文献
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Yongshun Zhao Shurong Sun Yongxiang Zhang 《Journal of Applied Mathematics and Computing》2017,53(1-2):183-199
In this paper, we investigate existence and generalized Hyers–Ulam–Rassias stability of Stieltjes quadratic functional integral equations. Firstly, we show some basic properties of the composite function of bounded variation. Secondly, we derive the generalized Hyers–Ulam–Rassias stability result after examining the existence and uniqueness results via the theory of measure of noncompactness and a fixed point theorem of Darbo type. Finally, two examples of functional integral equations of fractional order are given to demonstrate the applicability of our results. 相似文献
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Guoju Ye & Wei Liu 《数学研究》2016,49(4):433-448
This study presents a summary of the current state of research on the distributional
Henstock-Kurzweil integral. Basic properties such as integration by parts,
Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings,
Banach lattice, convergence theorems, fixed point theorems, are shown. This
study also summarizes its applications in integral and differential equations. 相似文献
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S. Heikkilä 《Journal of Mathematical Analysis and Applications》2011,379(1):171-179
In this paper we apply fixed point theorems for increasing mappings in ordered normed spaces to prove existence and comparison results for solutions of discontinuous functional differential and integral equations containing Henstock-Kurzweil integrable functions. 相似文献
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Tuo-Yeong Lee 《Czechoslovak Mathematical Journal》2009,59(4):1005-1017
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation
theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence
and equality of two iterated Henstock-Kurzweil integrals. 相似文献
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We consider a nonlinear system of integral equations describing the structure of a plane shock wave. Based on physical reasoning, we propose an iterative method for constructing an approximate solution of this system. The problem reduces to studying decoupled scalar nonlinear and linear integral equations for the gas temperature, density, and velocity. We formulate a theorem on the existence of a positive bounded solution of a nonlinear equation of the Uryson type. We also prove theorems on the existence and uniqueness of bounded positive solutions for linear integral equations in the space L 1[?r, r] for all finite r < +∞. For a more general nonlinear integral equation, we prove a theorem on the existence of a positive solution and also find a lower bound and an integral upper bound for the constructed solution. 相似文献
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S. Heikkilä 《Journal of Mathematical Analysis and Applications》2011,377(1):286-295
In this paper we prove monotone convergence theorems for Henstock-Kurzweil integrable functions from a compact real interval to an ordered Banach space. These theorems are then applied to prove existence results for solutions of a discontinuous functional integral equation containing Henstock-Kurzweil integrable functions. 相似文献
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Allan Peterson Bevan Thompson 《Journal of Mathematical Analysis and Applications》2006,323(1):162-178
We will study the Henstock-Kurzweil delta and nabla integrals, which generalize the Henstock-Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Henstock-Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases. 相似文献