• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.229-244
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• 2005

In this paper, we study the third order ordinary differential equation : $$x'(t)=f(t,x(t),x'(t),x'(t)),t{\in}(0,1)$$ subject to the boundary value conditions: $$x'(0)=x'(\xi),x'(1)=^{m-3}{\Sigma}_{i=1}{{\beta}x'({\eta}i),x'(1)=0}$$. Here ${\beta}_{i}{\in}R,\;^{m-3}{\Sigma}_{i=1}\;{\beta}_{i}\;=\;1,\;0<{\eta}_1<{\eta}_2<{\cdots}<{\eta}_{m-3}<1,\;0<\xi<1$. This is the case dimKer L = 2. When the ${\beta}_i$ have different signs, we prove some existence results for the m-point boundary value problem at resonance by use of the coincidence degree theory of Mawhin [12, 13]. Since all the existence results obtained in previous papers are for the case dimKerL = 1, our work is new.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.39-49
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• 2010

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

• The Korean Journal of Financial Management
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• v.1 no.1
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• pp.1-27
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• 1985

One of the most important research works in modern business enterpise is the relation between the purpose of business enterprise and decision making behavior of manager. It is because the coincidence of the former and the latter is considered an ideal type in evaluating the result of business management. Here I have set up assumptions in order to solve the above statements: (1) What purpose does the modern business enterprise set up and what kind of economic background does it have? (2) What is the theory of maximization of stock value among the purposes of business enterprise? (3) What kind of decision making do we do in the maximization of stock value in busiess administration? (4) How is the behavior of business financial manager's intention and decision made? The result pursued under the above assumptions shows that business manager's behavior of decision making is affected according to the degree that he gets some information, but basically is determined in consideration of his autonomous standpoint, namely the stability of business enterprise and the stability of manager himself while he faithfully performs his duty which is entrusted by stockholders. Therefore we come to the conclusion that there is a little gap between a manager's behavior of decision-making and the purpose of stock value maximization.