• 대한수학회지
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• 제39권3호
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• 대한수학회지
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• 제33권2호
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• 대한수학회지
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• 제34권1호
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• pp.247-255
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• 1997

In this paper, we are concerned with the existence of positive solutions for the boundary value problems of the form; $$(1) u"(t) + q(t)g(u(t)) = 0, 0 < t < 1 $$ $$ u(0) = 0 = u(1), $$ where q is singular at 0 and /or 1.or 1.

• Steel and Composite Structures
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• 제18권3호
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• pp.659-672
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• 2015

This research deals with the analytical solution of a curved beam with different shapes made of functionally graded materials (FGM's). It was assumed that modulus of elasticity is graded along the thickness direction of curved beam based on a power function. The beam was loaded under pure bending. Using the linear theory of elasticity, the general relation for radial distribution of radial and circumferential stresses of arbitrary cross section was derived. The effect of nonhomogeneity was considered on the radial distribution of circumferential stress. This behavior can be investigated for positive and negative values of nonhomogeneity index. The novelty of this study is application of the obtained results for different combination of material properties and cross sections. Achieved results indicate that employing different nonhomogeneity index and selection of various types of cross sections (rectangular, triangular or circular) can control the distribution of radial and circumferential stresses as designer want and propose new solutions by these options. Increasing the nonhomogeneity index for positive or negative values of nonhomogeneity index and for various cross sections presents different behaviors along the thickness direction. In order to validate the present research, the results of this research can be compared with previous result for reachable cross sections and non homogeneity index.

• 대한수학회지
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• 제53권2호
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• pp.305-313
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• 2016

In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

• 대한수학회보
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• 제50권3호
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• 대한수학회지
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• 제48권2호
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• pp.431-447
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• 2011

We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${\Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $\mathbb{R}^n$. We obtain a conclusion that, for n $\geq$ 3, -2 < $l_2$ < $l_1$ $\leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{\rightarrow}{\infty}}r^{\frac{2+l_1}{p-1}}\;u$ and $lim_{r{\rightarrow}0}r^{\frac{2+l_2}{q-1}}\;u$ always exist if $\frac{n+1_1}{n-2}$ < p < q, $p\;{\neq}\;\frac{n+2+2l_1}{n-2}$, $q\;{\neq}\;\frac{n+2+2l_2}{n-2}$. In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.

• 한국광학회지
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• 제18권4호
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• pp.256-263
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• 2007

SELFOC 소재를 사용하여 높은 수치구경을 가지는 광픽업용 대물렌즈를 설계하였다. SELFOC 소재는 radial gradient-index 분포를 가지며, 이것은 설계에 추가적인 자유도를 제공하므로, 비구면이 아닌 구면만으로 높은 수치구경의 대물렌즈의 설계가 가능하다. 이 연구에서는 quadratic constant와 광축의 굴절률, 광축 두께, 입사동 직경을 변화시키며 rms 스폿 직경 변화를 조사하였으며, Code V를 사용하여 대물렌즈의 최적화와 결상특성을 평가하였다. 이 분석에서는 quadratic constant와 광축의 굴절률이 클수록, 렌즈가 두꺼워질수록, 입사동 직경은 작을수록 더 좋은 특성을 보임을 알 수 있었다. 이 결과를 바탕으로 2매의 구면 SELFOC 렌즈로 구성된 높은 NA의 DVR용 대물렌즈를 설계하였으며, 2가지 형태의 해 Solution I, II가 존재하였다 Solution I은 두 매 모두 양의 굴절능을 가지며 compact한 광학계를 구성하지만, 비축 수차 보정이 Solution II에 비해 부족하였다. Solution II는 음-양의 굴절능으로 조합된 광학계로 비축 수차가 비교적 잘 보정되었지만, 광학계의 전장길이가 길고 렌즈의 직경이 커지는 문제점이 있었다.

• Bulletin of the Korean Chemical Society
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• 제17권2호
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• pp.188-192
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• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• Journal of Yeungnam Medical Science
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• 제4권1호
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• pp.145-149
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• 1987

경피요골동맥삽관후 수지괴사가 발생되어 손목을 절단한 1례를 보고하며, 동맥삽관후 수지괴사가 유발될 수 있는 요인으로는 사용된 카테터의 크기, 종류, 천자횟수, 삽관거치기간 및 카테터삽관후 유지방법외에도 환자의 혈액구성성분변화, 혈액응고장애, 심박출량감소상태, 성별 등을 들 수 있으며, 본원에서 발생된 예에서는 수술후 환자가 심히 움직여 끈으로 동맥삽관된 손목을 침대에 묶어 놓음으로써 카테터에 의한 혈관손상이 심했음이 가장 큰 원인일 것으로 추측되며 그 외에도 혈액성분변화 및 응고장애에 의해 심한 혈전형성이나 heparin용액의 간헐적 관류시 발생될 수 있는 혈전의 전색도 가능성이 있을 것으로 사료된다.