共查询到20条相似文献,搜索用时 15 毫秒
1.
本文考虑非线性常微分方程组周期解的存在性,得到了周期解的Nagumo型先验估计,由此在一般性条件下证明了方程组至少有一个T-周期解, 相似文献
2.
V. K. Romanko 《Differential Equations》2009,45(10):1429-1439
We study a spectral problem with two complex parameters for a normal linear system of second-order ordinary differential equations
on a closed interval with splitting or nonlocal boundary conditions. The results of this study are used to prove the existence
and uniqueness of a generalized solution of a boundary value problem in a cylinder for a class of partial differential equations. 相似文献
3.
中立型泛函微分方程的周期解 总被引:1,自引:1,他引:0
对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。 相似文献
4.
For abstract linear functional differential equations with a weighted pseudo-almost periodic forcing term, we prove that the existence of a bounded solution on R+ implies the existence of a weighted pseudo-almost periodic solution. Our results extend the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. To illustrate the results, we consider the Lotka-Volterra model with diffusion. 相似文献
5.
Pablo Amster Pablo De Nápoli 《Journal of Mathematical Analysis and Applications》2007,326(2):1236-1243
We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman-Lazer type conditions we prove the existence of at least one solution applying topological degree methods. We extend a celebrated result by Nirenberg for resonant systems. 相似文献
6.
Zhaoli Liu 《数学学报(英文版)》2000,16(3):505-514
Abstract
This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.
We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions
Research supported by the NNSF of China and the RFDP of China. 相似文献
7.
We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed. 相似文献
8.
In this paper, we establish a result of Leray-Schauder degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As applications, we prove the global existence of positive solutions for a multi-parameter system of second-order ordinary differential equations with respect to parameters. The discussion is based on the result of Leray-Schauder degree on the order interval and the fixed point index theory in cones. 相似文献
9.
K. K. Tam 《Studies in Applied Mathematics》1989,81(3):249-263
Traveling wave solutions are sought for a model of combustion in a porous medium. The problem is formulated as a nonlinear eigenvalue problem for a system of ordinary differential equations of order four, defined over an infinite interval. A shooting method is used to prove existence, and a priori bounds for the solution and parameters are obtained. 相似文献
10.
A. Yu. Ukhalov 《Mathematical Notes》1998,63(3):396-400
We consider a system of ordinary first-order differential equations. The right-hand sides of the system are proportional to
a small parameter and depend almost periodically on fast time and periodically on slow time. With this system, we associate
the system averaged over fast time. We assume that the averaged system has a structurally unstable periodic solution. We prove
a theorem on the existence and stability of almost periodic solutions of the original system.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 451–456, March, 1998. 相似文献
11.
《Journal of Computational and Applied Mathematics》2001,132(2):341-356
We prove the existence of positive solutions of second-order nonlinear differential equations on a finite interval with periodic boundary conditions and give upper and lower bounds for these positive solutions. Obtained results yield positive periodic solutions of the equation on the whole real axis, provided that the coefficients are periodic. 相似文献
12.
On solvability of non-linear semi-periodic boundary-value problem for system of hyperbolic equations
N. T. Orumbaeva 《Russian Mathematics (Iz VUZ)》2016,60(9):23-37
We study a non-linear semi-periodic boundary-value problem for a system of hyperbolic equations with mixed derivative. At that, the semi-periodic boundary-value problem for a system of hyperbolic equations is reduced to an equivalent problem, consisting of a family of periodic boundary-value problems for ordinary differential equations and functional relation. When solving a family of periodic boundary-value problems of ordinary differential equations we use the method of parameterization. This approach allowed to establish sufficient conditions for the existence of an isolated solution of non-linear semi-periodic boundary-value problem for a system of hyperbolic equations. 相似文献
13.
We consider issues related to the numerical solution of interval systems of ordinary differential equations. We suggest an algorithm that permits finding interval estimates of solutions with prescribed accuracy in reasonable time. The algorithm constructs an adaptive partition (a dynamic structured grid) based on a kd-tree over the space formed by interval initial conditions for the ordinary differential equations. In the operation of the algorithm, a piecewise polynomial function interpolating the dependence of the solution on the specific values of interval parameters is constructed at each step of solution of the original problem. We prove that the global error estimate linearly depends on the height of the kd-tree. The algorithm is tested on several examples; the test results show its efficiency when solving problems of the class under study. 相似文献
14.
Jean Mawhin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1987,38(2):257-265
The method of upper and lower solutions and convexity arguments are used to prove sharp results for the existence and multiplicity of periodic solutions for first order ordinary differential equations depending upon a parameter.Dedicated to Professor H. W. Knobloch for his sixtieth birthday 相似文献
15.
Xitao Yang 《Journal of Mathematical Analysis and Applications》2006,316(1):161-177
In this paper, we deal with a discrete predator-prey system with delay. We first give a sufficient condition for the uniform persistence of the system. Assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa's theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays, we obtain the existence of a periodic solution basing on the uniform persistence result. 相似文献
16.
We propose a new mathematical model of a repressilator, i.e., the simplest gene ring network consisting of three elements. The studied model is a three-dimensional system of ordinary differential equations depending on a single parameter. We study the existence and stability problems for relaxation periodic motion in this system. 相似文献
17.
We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions. 相似文献
18.
We establish conditions under which the existence of a periodic solution of a differential equation is preserved if a solution
of the corresponding difference equation possesses the same property. We prove the convergence of periodic solutions of a
system of difference equations to a periodic solution of a system of differential equations. Analogous problems are considered
for bounded solutions.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 989–996, July, 2005. 相似文献
19.
Katia A.G. Azevedo Marta C. Gadotti Luiz A.C. Ladeira 《Nonlinear Analysis: Theory, Methods & Applications》2007
We discuss the existence of periodic solutions to a system of differential equations with distributed delay which shows a certain type of symmetry. For this, such solutions are related to the solutions of a system of second-order ordinary differential equations. 相似文献
20.
We suggest an algorithm that permits one to prove the existence of limit periodic trajectories (cycles) in two-dimensional nonautonomous dissipative systems with periodic coefficients with the use of computational methods alone. We prove a fixed point theorem for two-dimensional mappings and describe methods of its application to two-dimensional nonautonomous systems with the use of the Poincaré mapping and interval arithmetics. 相似文献