In this paper we shall consider the nonlinear delay differential equation p0ðtÞ 1⁄4 bðtÞp mðt kxÞ 1þ pnðt kxÞ cðtÞpðtÞ; ð Þ where k is a positive integer, bðtÞ and cðtÞ are positive periodic functions of period x. In the nondelay case we shall show that (*) has a unique positive periodic solution pðtÞ, and we will study the global attractivity of pðtÞ. In the delay case we shall establish some ...

In this article, we discuss the applications of some fixed point theorems to various types of functional differential equations for proving the existence as well as global attractivity and ultimate positivity of solutions on unbounded intervals under some usual natural conditions. Our hypotheses and claims have also been explained with the help of some natural realizations. AMS (MOS) Subject Cl...

Abstract. In this paper, we study a non-autonomous n-species “pure-delay-type” competitive system, which can be seen as the generalization of the traditional “puredelay-type” Lotka-Volterra competition system. By constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the global attractivity of the positive solutions of the system are obtained. An example shows t...

The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.

In this paper, two classes of twoand three-dimensional Hopfield-type neural networks with time delays are considered by using a completely different method from known results. Some necessary and sharper sufficient criteria for the global attractivity of the equilibria of the neural networks are present.

In this paper, we consider an n-species Lotka-Volterra periodic competition system. Using a comparison method and the Brouwer fixed point theorem, we obtain some sufficient conditions for the ultimate boundedness of solutions and the existence and global attractivity of a positive periodic solution. We also point out that these results constitute a generalization of K. Gopalsamy and J. M. Cushi...

In this paper, we consider a discrete Nicholson’s blowflies model with delay. By constructing suitable Lyapunov functional, a sufficient condition for the permanence and global attractivity of the system is obtained. An example together with its numerical simulation shows the feasibility of our main results.