• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.593-611
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• 2008

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

• East Asian mathematical journal
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• 제34권5호
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• pp.683-691
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• 2018

We consider an optimal control problem for an impulsive stage-structured model involving ordinary differential equations with impulsive values of initial conditions in the next year. The main goal is to maximize a profit of the catch of Pacific cod in the South Korea through optimal harvest strategy as a control of adult cod. We established necessary conditions for the optimal harvest control using idea of Pontryagin's maximum principle. The optimal harvest strategy is to numerically solve the equation by using an iterative method with the Runge-Kutta method. Finally, we compare a monthly average of fishing mortality of Pacific cod from 2013 to 2017 with monthly fishing mortality for result obtained optimal harvest strategy.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.61-75
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• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.237-249
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• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.831-844
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• 2016

In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.

• 대한기계학회논문집A
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• 제26권3호
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• pp.487-496
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• 2002

Hydrodynamic behavior and response of vertical-cylindrical liquid-storage tank is considered. The equation of the liquid motion is shown by Laplace's differential equation with the fluid velocity potential. The solution of the Laplace's differential equation of the liquid motion is expressed with the modified Bessel functions. Only rigid tank is studied. The equivalent masses and heights for the tank contents are presented for engineering design model.

• 대한수학회논문집
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• 제24권2호
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• pp.215-226
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• 2009

For a class of Holling type II food chain systems with biological and chemical controls, we give conditions of the local stability of prey-free periodic solutions and of the permanence of the system. Further, we show the system is uniformly bounded.

• 대한수학회논문집
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• 제26권2호
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• pp.197-205
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• 2011

Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))'+px(t-{\tau})=0$, $t{\neq}t_{\kappa}$, ${\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0$, $c_i{\geq}0$, $i=1,2,{\ldots}n$, $p{\tau}$>0, $p_0{\tau}$>0, ${\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})$. Explicit sufficient and necessary condition are established when $c_i$ = 0, i = 1, 2, ${\ldots}$, n.