• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.665-685
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• 2000

The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.247-262
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

• Journal of the Korean Society for Nondestructive Testing
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• v.11 no.1
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• pp.13-22
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• 1991

In this paper, 3-dimensional fracture phenomena in the local area near a through notch tip located between the surface and the canter were investigated by using embedded dyeing grids with the pitch of $50.8{\mu}$. It was confirmed that displacement V and square root of distance from notch tip $y^{1/2}$ are not proportional in the local area of $\sqrt{{\mid}y{\mid}}\;<\;0.3mm^{1/2}$ and the maximum shea strain ${\varepsilon}_{xymax}$ near a notch tip occurred at the curvature beginning point of the notch curve. It was also noted that the maximum strain ${\varepsilon}_{xymax}$ in the thickness direction occurred at the interior, where the ratio of the distance measured from surface to the half of thickness of specimen is 0.3.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.47-52
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• 2003

To determine the effect of transverse open crack on the dynamic behavior of simply-supported Euler-Bernoulli beam with the moving masses, an iterative modal analysis approach is developed. The influence of depth and position of the crack in the beam, on the dynamic behavior of the simply supported beam system, have been studied by numerical method. The cracked section is represented by a local flexibility matrix, connecting two undamaged beam segments that is, the crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section, and is derived by applying a fundamental fracture mechanics theory. As the depth of the crack is increased, the mid-span deflection of the simply-supported beam, with the moving mass, is increased. The crack is positioned in the middle point of the pipe, and the mid-span defection of the simply-supported pipe represents maximum deflection.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.943-947
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• 1995

Assume that X is locally compact and Hausdorff. Then, we show that $\alpha X = sup {X \cup_f S(f)$\mid$f \in S^{\alpha}}$ for any compactification $\alpha X$ of X if and only if for any 2-point compatification $\gamma X$ of X with $\gamma X - X = {-\infty, +\infty}$, there exists a clopen subset A of \gamma X$ such that $-\infty \in A$ and $+\infty \notin A$. As a corollary, we obtain that if X is connected and locally connected, then $\alpha X = sup {X \cup_f S(f)$\mid$f \in S^{\alpha}}$ for any compactification $\alpha X$ of X if and only if X is 1-complemented.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.689-707
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• 2017

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f(z) holomorphic in the unit disc and f(0) = 0, f'(0) = 1 such that ${\Re}f^{\prime}(z)$ > ${\frac{1-{\alpha}}{2}}$, -1 < ${\alpha}$ < 1, we estimate a modulus of the second non-tangential derivative of f(z) function at the boundary point $z_0$ with ${\Re}f^{\prime}(z_0)={\frac{1-{\alpha}}{2}}$, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ${\mid}f^{{\prime}{\prime}}(z_0){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these inequalities is also proved.

• Journal of Adhesion and Interface
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• v.7 no.4
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• pp.18-23
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• 2006

The influence of the notch length on the stress distribution of mid-bondline and adherend was investigated using elasto-plastic finite element method. The results from the simulation showed that peak stress of mid-bondline decreased markedly as adherend with notch in the middle of lap zone, and the stress in the middle of joint with low stress originally increased evidently. All the peak stresses decreased firstly and increased again as the length of notch increased. The relative higher peak stress appeared at the point near the notch of adherend where might be failed previously during the loading procedure.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.82-85
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• 2006

In this study, the fatigue tests were performed on a series of reinforce concrete beams with type of aggregate to investigate the fatigue behavior. The four point loading system is used in the fatigue tests. In these tests, relations between the repeated loading cycles and mid-span deflections, number of repeated loading cycles when specimen was fractured were observed. On this basis, the mid-span deflections, the crack growth and failure mode of beams were studied. The result of tests, reinforce concrete beams with recycled aggregate were about similar failure mode with natural aggregate concrete beam.