• 대한수학회보
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• 제57권2호
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• pp.331-343
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• 2020

This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems -Δv = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ R^N : r₁ < |x| < r₂} with 0 < r₁ < r₂, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s₁(x)) = h(x, s₂(x)) = 0 for suitable positive, concave function s₁ and negative, convex function s₂, as well as sh(x, s) > 0 for s ∈ ℝ \ {0, s₁(x), s₂(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.

• Structural Engineering and Mechanics
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• 제4권1호
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• pp.49-59
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• 1996

This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. This highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum arc-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

• 대한수학회보
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• 제53권6호
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.440-444
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• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• Steel and Composite Structures
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• 제37권5호
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• pp.571-587
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• 2020

In this article the seismic demand and performance of two recent braced steel frames named steel moment frames with the elliptic bracing (ELBRFs) are assessed through a laboratory program and numerical analyses of FEM. Here, one of the specimens is without connecting bracket from the corner of the frame to the elliptic brace (ELBRF-E), while the other is with the connecting brackets (ELBRF-B). In both the elliptic braced moment resisting frames (ELBRFs), in addition to not having any opening space problem in the bracing systems when installed in the surrounding frames, they improve structure's behavior. The experimental test is run on ½ scale single-story single-bay ELBRF specimens under cyclic quasi-static loading and compared with X-bracing and SMRF systems in one story base model. This system is of appropriate stiffness and a high ductility, with an increased response modification factor. Moreover, its energy dissipation is high. In the ELBRF bracing systems, there exists a great interval between relative deformation at the yield point and maximum relative deformation after entering the plastic region. In other words, the distance from the first plastic hinge to the collapse of the structure is fairly large. The experimental outcomes here, are in good agreement with the theoretical predictions.

• 대한수학회보
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• 제51권1호
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• pp.139-156
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• 2014

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order k = 1 Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^2$-norm and order h in the $L^{\infty}$-norm for the control variable are proved.

• Korean Journal of Mathematics
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• 제12권1호
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• pp.77-90
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• 2004

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system of the Dirichlet problem on the bounded domain ${\Omega}$ in $R^n$. 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. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

• 대한수학회보
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• 제50권1호
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• pp.57-71
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• 2013

In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the ($p_1$, ${\cdots}$, $p_n$)-biharmonic systems. We use a variational approach based on a three critical points theorem due to Ricceri [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009), 3084-3089].

• 대한수학회지
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• 제37권4호
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• pp.565-577
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• 2000

We consider regularity questions arising in the degenerate elliptic vector valued variational inequalities -div(｜▽u｜p-2∇u)$\geq$b(x, u, ∇u) with p$\in$(1, $\infty$). It is a generalization of the scalar valued inequalities, i.e., the obstacle problem. We obtain the C1,$\alpha$loc regularity for the solution u under a controllable growth condition of b(x, u, ∇u).

• 한국자동차공학회논문집
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• 제10권3호
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• pp.176-184
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• 2002

The door stiffness is one of the important factors for the side impact. Generally, the researches have been conducted on the assembled door. A side impact door beam is installed in a door to protect occupants from the side impact. This research is only concentrated on the side impact beam and a side impact beam is designed. The cross section is defined to have an elliptic shape. An optimization problem is defined to find the design maximizing the intrusion stiffness within the specified weight. Design variables are the radii and the thickness of the ellipsoid. The analysis of the side impact is carried out by the nonlinear finite element method. The optimization problem is solved by two methods. One is the experimental design scheme using an orthogonal array. The other is the gradient-based optimization using the response surface method(RSM). Both methods have obtained the better designs than the current one.