Positive solutions for a scalar differential equation with several delays

For a scalar delay differential equation , we obtain new explicit conditions for the existence of a positive solution.     

Asymptotic constancy for a differential equation with multiple state-dependent delays

In this paper, we investigate the asymptotic behavior of solutions to a differential equation with multiple state-dependent delays. It is shown that every bounded solution of such an equation tends to a constant as t→∞. Our results improve and extend some corresponding ones already known.     

Periodic solutions in general scalar non-autonomous models with delays

Theorems for the existence of periodic solutions for diverse models of population dynamics are obtained as corollaries of a few basic theorems, thus unifying the analysis of a broad class of scalar models in a single setting. The latter mechanism allows to obtain existence conditions for a broad class of nonlinear, non-autonomous models and models with state-dependent delays. The technique fulfills multiple roles: it can be used to expand on well-known results as well as to shorten existing proofs. We provide some examples which illustrate the applicability of our results.     

具分布时滞的一类Logistic方程的周期正解

利用重合度定理,建立了下面具分布时滞的Logistic方程x'(t)=x(t)∑ni=1ri(t)1-(1)/(K(t))∫t-∞x(s)dsRi(t,s)正周期存在的充分条件.其中ri(t),K(t)和Ri(t,s)是以ω＞0为周期的正周期函数.     

Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves

The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f″(u)?0, is considered with an assumption . We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L¹ norm with the optimal convergence order of O(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included.     

Asymptotic solutions to a discrete airy equation

A nonstandard finite difference scheme for the Airy equation leads to a linear, second—order difference equation for which the theorems of Poincaré and Perron do not apply if asymptotic representations of the solutions are desired. Using the method of dominant balance, a suggested form for the asymptotic solutions is obtained. This relation is then used to construct the required asymptotic representations for the two linearly independent solutions     

Some properties of solutions of a scalar Riccati equation with complex coefficients

We give the definition of normal and limit solutions of the Riccati equation with complex coefficients and study some properties of these solutions. We prove the minimality property of a solution of a system of two linear first-order ordinary differential equations.     

Analysis of solutions of a nonlinear scalar field differential equation

We consider a nonlinear differential equation arising in mathematical models of elementary particle theory. For this equation, we examine questions of the extendability of solutions, the boundedness of solutions at infinity, and the search for new conditions for the existence of a positive particle-like solution.     

Asymptotic behavior of solutions of a three-species predator-prey model with diffusion and time delays

In this paper, we deal with a reaction-diffusion system with time delays arising from a three-species predator-prey model under the homogeneous Neumann boundary conditions, and study the asymptotic behavior of solutions.     

Asymptotic behavior of solutions of a second-order nonlinear differential equation

Asymptotic properties of proper solutions of a certain class of essentially nonlinear binomial differential equations of the second order are investigated.     

Long time behavior of solutions for a scalar nonlocal reaction-diffusion equation

In this paper we study the long time behavior of the solution for a scalar nonlocal reaction-diffusion equation, in which the nonlocal term acts to conserve the spatial integral of the power of the unknown function as time evolves. A class of initial data is found to guarantee the existence of positive global solutions and the convergence to some steady states. A sufficient condition for positive global solutions to be unbounded is also given.     

On convergence of the solutions of a functional differential equation

A sufficient condition is given for the solutions of a functionally perturbed linear system of ordinary differential equations to have limits at ± ∞.