Positive solutions for 2p-order and 2q-order nonlinear ordinary differential systems

In this paper, by using Krasnosel'skii fixed point theorem and under suitable conditions, we present the existence of single and multiple positive solutions to the following systems:

     

Two periodic solutions of second-order neutral functional differential equations

In this paper, we consider a type of second-order neutral functional differential equations. We obtain some existence results of multiplicity and nonexistence of positive periodic solutions. Our approach is based on a fixed point theorem in cones.     

Positive periodic solutions of functional differential equations

We consider the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x(t)−λb(t)f(x(t−τ(t))), where are ω-periodic, , , f,g∈C([0,∞),[0,∞)), and f(u)>0 for u>0, g(x) is bounded, τ(t) is a continuous ω-periodic function. Define , , i₀=number of zeros in the set and i_∞=number of infinities in the set . We show that the equation has i₀ or i_∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively.     

Existence of multiple positive periodic solutions for functional differential equations

In our paper, by employing Krasnoselskii fixed point theorem, we investigate the existence of multiple positive periodic solutions for functional differential equations

     

非线性微分方程的正周期解

§ 1　 IntroductionIn[1 ] ,Saker and Agarwal studied the existence and uniqueness of positive periodicsolutions of the nonlinear differential equationN′(t) =-δ(t) N(t) + p(t) N(t) e- a N(t) ,(1 )whereδ(t) and p(t) are positive T-periodic functions.They proved that if p* >δ* ,then(1 ) has a unique T-periodic positive solution,wherep* =min0≤ t≤ Tp(t) ,δ* =max0≤ t≤ Tδ(t) .　　In view ofthe papermentioned above,whatcan be said aboutequation(1 ) when p* ≤δ* ?In this paper,we conside…     

Positive periodic solutions of nonautonomous functional differential systems

Considered is the periodic functional differential system with a parameter, x^′(t)=A(t,x(t))x(t)+λf(t,xt). Using the eigenvalue problems of completely continuous operators, we establish some criteria on the existence of positive periodic solutions. Moreover, we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions, which are compared with existing ones.     

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.     

Global positive periodic solutions of periodic n-species competition systems

In this paper, an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems is obtained. It improves a series of the well-known sufficiency theorems in the literature about the problems mentioned above. The method is based on a well-known fixed point theorem in a cone of Banach space. This approach can be applied to more general competition systems.     

Approximate periodic solutions of a nonlinear parabolic system and an identification problem

This work continues our study in [L. Lei, Identification of parameters through the approximate periodic solutions of a linear parabolic system, preprint, 2005] on the identification problem for the coefficients for the lower order terms in a parabolic system, through its approximate periodic solutions. Different from the work in [L. Lei, Identification of parameters through the approximate periodic solutions of a linear parabolic system, preprint, 2005], our system now is nonlinear and the coefficients to be detected are from the first order term. From the application point of view, we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain. The existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper.     

Positive periodic solutions of higher-dimensional nonlinear functional difference equations

By using a well-known fixed point index theorem, we study the existence, multiplicity and nonexistence of positive T-periodic solution(s) to the higher-dimensional nonlinear functional difference equations of the form

     

Existence of positive periodic solutions of first order neutral differential equations with variable coefficients

This work deals with the existence of positive $\omega$-periodic solutions for the first order neutral differential equation. The results are established using Krasnoselskii’s fixed point theorem. An example is given to support the theory.     

Positive solutions of nonlinear singular third-order two-point boundary value problem

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem

     

Positive periodic solutions for a nonlinear differential system with two parameters

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.     

Multiple positive periodic solutions of nonlinear functional differential system with feedback control

In this paper, we employ Avery-Henderson fixed point theorem to study the existence of positive periodic solutions to the following nonlinear nonautonomous functional differential system with feedback control:

     

Positive solutions for a second-order differential system

This paper investigates the existence of positive solutions for a second-order differential system by using the fixed point theorem of cone expansion and compression.     

Nonnegative doubly periodic solutions for nonlinear telegraph system

This paper deals with the nonnegative doubly periodic solutions for nonlinear telegraph system

     

Volterra积分微分方程周期正解的一个新的存在性理论

该文通过使用锥不动点定理,研究了一类非自治Volterra积分微分方程周期正解的一个新的存在性理论,把一般结果应用于几类具时滞的生物数学模型时,改进了一些已知结果,并得到了一些新的结果.