• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.797-804
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• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• 대한기계학회논문집A
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• 제24권6호
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• pp.1529-1539
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• 2000

A newly developed optimization method which uses the genetic algorithm combined with the sensitivity analysis is presented in this paper. The genetic algorithm is a probabilistic method, searching the optimum at several points simultaneously, requiring only the values of the object and constraint functions. It has therefore more chances to find global solution and can be applied various problems. Nevertheless, it has such shortcomings that even it approaches the optimum rapidly in the early stage, it slows down afterward and it can't consider the constraints explicitly. It is only because it can't search the local area near the current points. The traditional method, on the other hand, using sensitivity analysis is of great advantage in searching the near optimum. Thus the combination of the two techniques makes use of the individual advantages, that is, the superiority both in global searching by the genetic algorithm and in local searching by the sensitivity analysis. Application of the method to the several test functions verifies that the method suggested is very efficient and powerful to find the global solutions, and that the constraints can be considered properly.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.843-848
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• 2014

In this paper, we investigate the boundedness character, the periodic character and the global behavior of positive solutions of the difference equation $$x_{n+1}=p_n+\frac{x_n}{x_{n-1}},\;n=0,1,{\cdots}$$ where $\{p_n\}$ is a two periodic sequence of nonnegative real numbers and the initial conditions $x_{-1}$, $x_0$ are arbitrary positive real numbers.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 추계 학술대회
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• pp.351-359
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• 2006

Author considered the contradiction of Capitalism and its solution, systemized the concept to newly define ethics management and social responsibility whose various terminologies are used in domestic and foreign country and compared, analyzed and considered global guideline. Standard organization and global evaluation model of internationally-performed ethics management on the basis of the concept of new ethics management.

• 충청수학회지
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• 제26권3호
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• pp.631-639
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• 2013

We investigate the existence of a global attractor for the Cauchy problem $$x^{\prime}(t)=Ax(t)+F(x(t)),\;x(0)=x_0{\in}X$$ on a Banach space X according to the remark in You and Yuan's paper.

• 대한수학회논문집
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• 제27권1호
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권1호
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• pp.17-28
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• 2013

In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type functional impulsive integrodifferential equations. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• 대한수학회논문집
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• 제37권2호
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• 대한수학회지
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• 제58권5호
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.