• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.377-385
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• 2002

In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system $\Delta$u+u($g_1$(u)-$g_2$(v))=0 $\Delta$u+u($h_1$(u)-$h_2$(v))=0 in$R_{+}$ $\times$ $\Omega$, $u\mid\partial\Omega = u\mid\partial\Omega = 0$. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.305-314
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• 2006

In this paper, we consider the oscillation of first order sublinear difference equation with positive neutral term $\Delta(\chi(n)+p(n)\chi(\tau(n)))+f(n,\chi(g1(n)),\cdots,\chi(gm(n)))=0$. We obtain necessary and sufficient conditions for the solutions of this equation to be oscillatory.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.65-73
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• 2003

In this paper we seek a positive, radially symmetric and energy minimizing solution of an m-Laplacian equation, -div$($\mid${\nabla}u$\mid$^{m-2}$\mid${\nabla}u)\;=\;h(u)$. In the variational sense, the solutions are the critical points of the associated functional called the energy, $J(v)\;=\;\frac{1}{m}\;\int_{R^N}\;$\mid${\nabla}v$\mid$^m\;-\;\int_{R^N}\;H(v)dx,\;where\;H(v)\;=\;{\int_0}^v\;h(t)dt$. A positive, radially symmetric critical point of J can be obtained by solving the constrained minimization problem; minimize{$\int_{R^N}$\mid${\nabla}u$\mid$^mdx$\mid$\;\int_{R^N}\;H(u)d;=\;1$}. Moreover, the solution minimizes J(v).

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1357-1368
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• 2014

This paper is concerned with a reaction-diffusion single species model with harvesting on n-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.711-721
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• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.749-755
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• 2009

In this paper, we investigate the invariant interval, periodic character, semicycle and global attractivity of all positive solutions of the equation $Y_{n+1}\;=\;\frac{p+qy_{n-k}}{1+y_n+ry_{n-k}}$, n = 0, 1, ..., where the parameters p, q, r and the initial conditions $y_{-k}$, ..., $y_{-1}$, $y_0$ are positive real numbers, k $\in$ {1, 2, 3, ...}. It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002]

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.895-902
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• 2009

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

• Laser Solutions
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• v.14 no.1
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• pp.25-29
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• 2011

Micromachining of photosensitive glass by UV exposure, heat treatment, and etching processes is reported. Like photoresist, the photosensitive glass is also classified into positive and negative types by development characteristics. For the positive type, the exposed area is crystallized and etched away during the etching process in HF solution, whereas the unexposed area is crystallized and etched away for the negative type. The crystallized area of the photosensitive glass has an etch rate approximately 30~100 times faster than that of the amorphous area so that it becomes possible to fabricate microstructures in the glass. Based on the unique properties of glass such as high optical transparency, electrical insulation, and chemical/thermal stability, the glass micromachining technique introduced in this work could be widely applied to various devices in the fields of electronics, bio engineering, nanoelectonics and so on.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.349-357
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• 2002

In this paper, we analyze queueing behaviors and investigate the possibilities of reducing and controlling shortages and oversupplies in the bidirectional queueing system which forms a negative queue by demand and a positive queue by supply. Interarrival times of units in the bidirectional queueing system investigated are exponetially distributed. Instant pairing off implies that queue can be either positive or negative, but not both at the same time. The results include a proof that sum of queue lengths is minimized if rates of demand and supply in each system are equal and optimum solutions for rates of supply which minimize the sum of queue lengths when rates of demand and sum of rates of supply are given. In addition, the relationship between the ordinary queueing system and the bidirectional queueing system is investigated.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1323-1329
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• 2010

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).