共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article, we investigate a nonlinear system of differential equations with two parameters
$$\left\{ \begin{array}{l} x"(t)=a(t)x(t)-\lambda f(t, x(t), y(t)),\y"(t)=-b(t)y(t)+\mu g(t, x(t), y(t)),\end{array}\right.$$
where $a,b \in C(\textbf{R},\textbf{R}_+)$ are $\omega-$periodic for some period $\omega > 0$, $a,b \not\equiv 0$, $f,g \in C(\textbf{R} \times \textbf{R}_+ \times \textbf{R}_+ ,\textbf{R}_+)$ are $\omega-$periodic functions in $t$, $\lambda$ and $\mu$ are positive parameters. Based upon a new fixed point theorem, we establish sufficient conditions for the existence and uniqueness of positive periodic solutions to this system for any fixed $\lambda,\mu>0$. Finally, we give a simple example to illustrate our main result. 相似文献
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In this paper, we develop Kaplan-Yorke's method and consider the existence of periodic solutions for delay differential equations with two delays. Especially, we study Hopf and saddle-node bifurcations of periodic solutions for the equation with parameters, and give conditions under which the bifurcations occur. 相似文献
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Jurang Yan 《Journal of Mathematical Analysis and Applications》2007,327(2):854-868
In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established. 相似文献
8.
Shun Shimomura 《Journal of Mathematical Analysis and Applications》2005,304(2):644-651
We treat a Riccati differential equation w′+w2+p(z)=0, where p(z) is a nonconstant doubly periodic meromorphic function. Under certain assumptions, every solution is meromorphic in the whole complex plane. We show that the growth order of it is equal to 2, and examine the frequency of α-points and poles. Furthermore, the number of doubly periodic solutions is discussed. 相似文献
9.
Hans-Otto Walther 《Annali di Matematica Pura ed Applicata》2006,185(4):577-611
We consider a one-parameter family of delay differential equations which has been proposed as a model for a prize and prove
that at a critical parameter where the linearization at equilibrium has a double zero eigenvalue periodic solutions bifurcate
off with periods descending from infinity.
AMS Subject Classification. 34K18,34K13,37G15 相似文献
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In this paper, we study the existence, multiplicity and nonexistence of positive ω-periodic solutions for a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones. Some new results are obtained. As an application of our results, we discuss the existence of a positive periodic solution for a class of models of blood cell production with a parameter, which has not been investigated by using previous methods. 相似文献
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Xuerong Mao 《Journal of Theoretical Probability》1991,4(1):161-167
We give here some criterions for the existence and uniqueness of a global solution to a stochastic differential equation based on a semimartingale with spatial parameters of the form
相似文献
13.
In this work, we propose a conjecture about the stability of the periodic solutions of the Ricker equation with periodic parameters, which goes beyond the existing theory, and for the special case of period-two parameters we analytically show the conjecture is true. For this case we show that the stability region in parameter space obtained from the conjecture is larger than a previously proposed stability region. The period-three case is investigated numerically and similar extensions are realized. This suggests that the current theory cited in this paper, while giving sufficient conditions for stability is far from optimal. 相似文献
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Criterion of periodicity of solutions of a certain differential equation with a periodic coefficient
F. Neuman 《Annali di Matematica Pura ed Applicata》1967,75(1):385-396
Summary In this paper the differential equation (1) y″=q(t)y is considered where q(t) is a real continuous function with period π.
There is proved a necessary and sufficient condition for the stability of the trivial solution of Equation (1) when the zeros
of the characteristic equation λ2 - Aλ+1=0, coincide. Moreover, there is shown the construction of all Equations (1) admitting only periodic or half-periodic
solutions with period π. 相似文献
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Zhengxin Zhou 《Journal of Applied Mathematics and Computing》2008,27(1-2):85-95
In this article, we use a new method—reflecting function to study the existence of periodic solutions of some periodic systems with small parameters. 相似文献
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We obtain deterministic first-order linear differential equations with ordinary and variational derivatives and deterministic initial conditions for the expectation and the second moment function of the solution of an ordinary scalar first-order linear inhomogeneous differential equation whose coefficients are random processes. We derive existence conditions for mean periodic solutions. In particular, we consider Gaussian and uniformly distributed random coefficients. 相似文献
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A note on decay properties for the solutions of a class of partial differential equation with memory
Zai-yun Zhang Zhen-hai Liu Xiu-jin Miao Yue-zhong Chen 《Journal of Applied Mathematics and Computing》2011,37(1-2):85-102
The purpose of this article is to study decay properties for solutions of a class of PDEs with memory by Lyapunov functionals method. Moreover, we prove that when the kernels of the convolutions decay exponentially, the first and second order energy of the solutions decay exponentially. Also we show that when the kernels decay polynomially, these energies decay polynomially. 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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GuiZhanji GeWeigao 《高校应用数学学报(英文版)》2005,20(1):59-63
By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solutions of a kind of third-order neutral delay functional differential equation with deviating arguments. 相似文献
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