• 충청수학회지
• /
• 제27권3호
• /
• pp.503-511
• /
• 2014

In this paper, we investigate the role of nonlocal interaction energy on nucleations of periodic solutions in a one-dimensional problem arising in smectic liquid crystals.

• 대한수학회지
• /
• 제50권6호
• /
• pp.1165-1181
• /
• 2013

In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].

• Kyungpook Mathematical Journal
• /
• 제60권2호
• /
• pp.401-413
• /
• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• Korean Journal of Mathematics
• /
• 제22권3호
• /
• pp.471-489
• /
• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• Journal of applied mathematics & informatics
• /
• 제31권3_4호
• /
• pp.577-594
• /
• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• 품질경영학회지
• /
• 제31권3호
• /
• pp.193-204
• /
• 2003

In this paper, we consider a periodic preventive maintenance(PM) policy in which each PM reduces the hazard rate but remains the pattern of hazard rate unchanged. And the system undergoes only minimal repairs at failures between PM's. The expected cost rate per unit time is obtained. The optimal number N of PM and the optimal period x, which minimize the expected cost rate per unit time are discussed. Explicit solutions for the optimal periodic PM are given for the Weibull distribution case.

• 대한수학회보
• /
• 제49권6호
• /
• pp.1223-1240
• /
• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• 충청수학회지
• /
• 제30권3호
• /
• pp.323-329
• /
• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• Kyungpook Mathematical Journal
• /
• 제49권2호
• /
• pp.299-312
• /
• 2009

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.

• 충청수학회지
• /
• 제34권3호
• /
• pp.221-234
• /
• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.