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1.
K. S. Lapin 《Differential Equations》2018,54(1):38-48
We introduce several generalizations of the properties of equiboundedness and uniform boundedness of solutions of ordinary differential systems, which are united by the common names of equiboundedness in the sense of Poisson and uniform boundedness in the sense of Poisson. For each of the above-introduced properties, we use the method of Lyapunov vector functions to obtain sufficient criteria for the system to have a certain property. In terms of the upper Dini derivative of the Lyapunov function given by a system, several criteria are established for the solutions of this system to have the relevant type of uniform boundedness in the sense of Poisson. 相似文献
2.
K. S. Lapin 《Differential Equations》2013,49(10):1246-1251
We introduce the notions of equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables for solutions with partly controlled initial conditions. We obtain sufficient conditions for the equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables of solutions with partly controlled initial conditions. We introduce the notions of equiboundedness and uniform boundedness with respect to part of the variables for solutions of systems with partly controlled initial conditions. We obtain sufficient conditions for the equiboundedness and uniform boundedness with respect to part of the variables of solutions with partly controlled initial conditions. 相似文献
3.
K. S. Lapin 《Siberian Mathematical Journal》2018,59(6):1100-1104
Using the higher-order derivatives of Lyapunov functions, we obtain sufficient tests of various types for the uniform-ultimate boundedness in the sense of Poisson of solutions and various types of equiultimate boundedness of solutions in the sense of Poisson. 相似文献
4.
K. S. Lapin 《Differential Equations》2016,52(5):549-556
On the basis of the method of Lyapunov vector functions, we obtain a sufficient test for the uniform partial boundedness of solutions with partially controlled initial conditions. We introduce the notions of partial equiboundedness, partial equiboundedness in the limit, and partial uniform boundedness in the limit of solutions with partially controlled initial conditions. By the method of Lyapunov vector functions, we obtain sufficient tests for the partial equiboundedness of solutions and for the partial uniform boundedness in the limit and partial equiboundedness in the limit of solutions with partially controlled initial conditions. 相似文献
5.
K. S. Lapin 《Mathematical Notes》2016,99(1-2):253-260
The notions of partial total boundedness of solutions with partially controlled initial conditions and of partial total equiboundedness of solutionswith partially controlled initial conditions are introduced. The direct Lyapunov method and the method of Lyapunov vector functions are used to obtain sufficient conditions for these types of boundedness of the solutions. 相似文献
6.
We introduce the notions of Poisson total boundedness of solutions, partial Poisson total boundedness of solutions, and partial Poisson total boundedness of solutions with partly controlled initial conditions. We use the Lyapunov vector function method to obtain sufficient conditions for the Poisson total boundedness of solutions, the partial Poisson total boundedness of solutions, and the partial Poisson total boundedness of solutions with partly controlled initial conditions. As a consequence, we obtain sufficient conditions for the above-mentioned kinds of Poisson total boundedness of solutions based on the Lyapunov function method.
相似文献7.
Mathematical Notes - The notions of Poisson boundedness and Poisson partial boundedness of solutions of systems are introduced. Based on the Lyapunov function method and... 相似文献
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Mathematical Notes - The notions of different types of boundedness in the sense of Poisson of solutions to systems of differential equations are introduced. Sufficient conditions are obtained for... 相似文献
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讨论了具有无限时滞的Volterra积分方程的周期解和一致最终有界性.把泛函微分方程中的一个著名定理,即一致有界性和一致最终有界性保证周期解的存在性,推广到积分方程. 相似文献
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Timothy A. Ademola 《Applied mathematics and computation》2010,216(10):3044-3049
Sufficient conditions for the existence of solutions to boundedness and ultimate boundedness problems associated to a certain third order nonlinear differential equation are given by means of the Lyapunov’s second method. The appropriate Lyapunov function is given explicitly. Our results complement some well known results on the third order differential equations in the literature. 相似文献
14.
Further results on the bounedness and periodicity of some differential equations of the fourth order
A. M. A. Abou-El-Ela 《应用数学学报(英文版)》1985,2(3):241-246
This research investigates the ultimate boundedness of solutions of the differential equations of the form (1.1), where the bounding constant is independent of the initial values of solutions. An existence result for periodic solutions of (1.1) is also established. 相似文献
15.
Zhidong Teng 《Journal of Differential Equations》2002,179(2):538-561
The paper studies the general nonautonomous Lotka-Volterra multispecies systems with finite delays. The ultimate boundedness, permanence, global attractivity, and existence and uniqueness of strictly positive solutions, positive periodic solutions, and almost periodic solutions are obtained. These results are basically an extension of the known results for nonautonomous Lotka-Volterra multispecies systems without delay to systems with delay. 相似文献
16.
Ethelbert Nwakuche Chukwu 《Annali di Matematica Pura ed Applicata》1975,104(1):123-149
Summary This research investigates the boundedness, as t→∞, of solutions of the third order order differential equation 2.1(1). Special
attention is drawn to a method in current usage which rests on the existence of appropriate Yoshizawa function with which
ultimate boundedness is proved for all solutions of 2.1(1) under quite mild restraints on f, g, h and p.
Entrata in Redazione il 23 maggio 1973. 相似文献
17.
高维系统周期解的存在性与唯一性 总被引:1,自引:0,他引:1
本文首先利用一种新方法讨论高维系统解的一致有界性,一致最终有界性及非常稳定性问题,然后将所获结果应用于高维系统周期解的存在性与唯一性的研究。另外,本文还提出了“阶梯形系统”的概念,并对其建立了一种利用系统部分方程周期解存在性判定整个系统周期解存在性的方法。 相似文献
18.
M. A. Asmussen 《Annali di Matematica Pura ed Applicata》1971,89(1):121-143
Summary In this paper three new results are obtained for equations of the form (1.1). Conditions are established which guarantee asymptotic
stability, ultimate boundedness, and convergence of solutions of (1.1).
This work was supported by the National Science Foundation COSIP (GY 4754).
Entrata in Redazione il 12 ottobre 1970. 相似文献
19.
In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems. 相似文献
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