• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.875-883
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• 2009

At least two positive solutions of a first-order periodic boundary value problem with impulse are obtained by establishing a new cone and the theorem of fixed point index. And at the end of this paper we give an example to illustrate the application of our main results.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.259-271
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• 2006

We consider a semilinear elliptic boundary value problem with Dirichlet boundary condition $Au+bu^+-au^-=t_{1{\phi}1}+t_{2{\phi}2}$ in ${\Omega}$ and ${\phi}_n$ is the eigenfuction corresponding to ${\lambda}_n(n=1,2,{\cdots})$. We have a concern with the multiplicity of solutions of the equation when ${\lambda}_1$ < a < ${\lambda}_2$ < b < ${\lambda}_3$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.5
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• pp.731-739
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• 1987

This study has been performed on multiple steady-state natural convection in the upflow region induced by an inclined isothermal plate immersed in pure cold water. The newly found additional steady-state solutions are of considerable practical interest because the heat-transfer rates for a pair of solutions with determining physical parameters and boundary conditions otherwise identical are sometimes vastly different. The results are as follows: First, in the largely upflow region, two solutions exist for 0.15157

• Journal of the military operations research society of Korea
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• v.6 no.2
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• pp.69-88
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• 1980

A stochastic fundamental duel with continous interfiring times is considered for including the kill effect of multiple hits and fixed duel time. Two alternatives, 'vital hit' and 'damage coefficient' approaches, are developed. Since a large quantity of ammunition is consumed when a sure kill is obtained through repetitive multiple hits, limitation of initial ammunition supply is included in the stochastic duel models with multiple hits and fixed duel time. General solutions are obtained and examples with negative exponential interfiring times and geometric ammunition supply are given.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.837-844
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• 2010

In this paper, a class of initial value problem of hyperbolic equations for fourth order with multiple characteristics is considered and can be solved analytically by variable transforms. Also, similar to Goursat's problem we present a direct integration technique for finding a new solutions of an inhomogeneous hyperbolic equation of fourth order such that the attached conditions are given on its multiple characteristics.

• KIEAE Journal
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• v.16 no.1
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• pp.81-87
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• 2016

Purpose: Heat transfers phenomena are described by the second order partial differential equation and its boundary conditions. In a three-dimensional structure of a building, the heat transfer phenomena generally include more than one material, and thus, become complicate. The analytic solutions are useful to understand heat transfer phenomena, but they can hardly be applied in engineering or design problems. Engineers and designers have generally been forced to use numerical methods providing reliable results. Finite volume methods with the unstructured grid system is only the suitable means of the analysis for the complex and arbitrary domains. Method: To obtain an numerical solution, a discretization method, which approximates the differential equations, and the interpolation methods for temperature and heat flux between two or more materials are required. The discretization methods are applied to small domains in space and time, and these numerical solutions form the descretized equations provide approximated solutions in both space and time. The accuracy of numerical solutions is dependent on the quality of discretizations and size of cells used. The higher accuracy, the higher numerical resources are required. The balance between the accuracy and difficulty of the numerical methods is critical for the success of the numerical analysis. A simple and easy interpolation methods among multiple materials are developed. The linear equations are solved with the BiCGSTAB being a effective matrix solver. Result: This study provides an overview of discretization methods, boundary interface, and matrix solver for the 3-dimensional numerical heat transfer including two materials.

• Journal of the Korean Mathematical Society
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• v.31 no.1
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• pp.11-28
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• 1994

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.141-152
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• 2003

Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant's path criterion derived on a thermodynamics basis.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.1-14
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• 2007

Because of complexity, the literature regarding the free vibration analysis of a Timoshenko beam carrying "multiple" spring-mass systems is rare, particular that regarding the "exact" solutions. As to the "exact" solutions by further considering the joint terms of shear deformation and rotary inertia in the differential equation of motion of a Timoshenko beam carrying multiple concentrated attachments, the information concerned is not found yet. This is the reason why this paper aims at studying the natural frequencies and mode shapes of a uniform Timoshenko beam carrying multiple intermediate spring-mass systems using an exact as well as a numerical assembly method. Since the shear deformation and rotary inertia terms are dependent on the slenderness ratio of the beam, the shear coefficient of the cross-section, the total number of attachments and the support conditions of the beam, the individual and/or combined effects of these factors on the result are investigated in details. Numerical results reveal that the effect of the shear deformation and rotary inertia joint terms on the lowest five natural frequencies of the combined vibrating system is somehow complicated.