• Korean Journal of Mathematics
• /
• 제21권1호
• /
• pp.81-90
• /
• 2013

We investigate the bounded weak solutions for the Hamiltonian system with bounded nonlinearity decaying at the origin and periodic condition. We get a theorem which shows the existence of the bounded weak periodic solution for this system. We obtain this result by using variational method, critical point theory for indefinite functional.

• 충청수학회지
• /
• 제27권4호
• /
• pp.707-720
• /
• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• 충청수학회지
• /
• 제31권1호
• /
• pp.53-64
• /
• 2018

This paper deals with the study of solutions for the elliptic system with jumping nonlineartity and growth nonlinearity and Dirichlet boundary condition. We apply the two critical point theorem when proving the existence of nontrivial solutions for the elliptic system. We define the energy functional associated to the elliptic system and prove that the functional has two critical values.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권2호
• /
• pp.199-212
• /
• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

• 전력전자학회논문지
• /
• 제24권4호
• /
• pp.244-258
• /
• 2019

The reliability of power electronic systems becomes increasingly important, as power electronic systems have gradually gained an essential status in a wide range of industrial applications. Accordingly, recent research has made an effort to improve the reliability of power electronic systems to comply with stringent constraints on safety, cost, and availability. The condition monitoring of power electronic components is one of the main topics in the research area of the reliability of power electronic systems. In this paper, condition-monitoring methods of reliability-critical components in power electronic systems are discussed to provide the current state of knowledge by organizing and evaluating current representative literature.

• Geomechanics and Engineering
• /
• 제8권2호
• /
• pp.237-255
• /
• 2015

From the related engineering principles, analytical solutions for horizontal crack initiation and propagation on a coal panel floor-underlying strata interface due to coal panel excavation are derived in this paper. Two important concepts, namely the critical panel width of horizontal crack initiation on the panel floor-underlying strata interface and the critical panel width of vertical fracture (crack) initiation in the panel floor, have been presented. The resulting analytical solution indicates that: (1) the first criterion can be used to express the condition under which horizontal plane cracks (on the panel floor-underlying strata interface or in the panel floor because of delamination) due to the mining induced vertical stress will initiate and propagate; (2) the second criterion can be used to express the condition under which vertical plane cracks (in the panel floor) due to the mining induced horizontal stress will initiate and propagate; (3) this orthogonal set of horizontal and vertical plane cracks, once formed, will provide the necessary weak network for the flow of gas to inrush into the panel. Two characteristic equations are given to quantitatively estimate both the critical panel width of vertical fracture initiation in the panel floor and the critical panel width of horizontal crack initiation on the interface between the panel floor and its underlying strata. The significance of this study is to provide not only some theoretical bases for understanding the fundamental mechanism of a longwall floor gas inrush problem but also a benchmark solution for verifying any numerical methods that are used to deal with this kind of gas inrush problem.

• 대한수학회보
• /
• 제36권4호
• /
• pp.637-647
• /
• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• 한국지반공학회:학술대회논문집
• /
• 한국지반공학회 2004년도 춘계학술발표회
• /
• pp.380-387
• /
• 2004

Recently the geosynthetics reinforced retaining wall has been widely used instead of the steel reinforced retaining wall. The geosynthetics reinforced retaining wall is a very dangerous structure if the geosynthetics lose their strength about tension or if it lose their pullout resistence, but it was known that the geosynthetics reinforced wall had a great resistence and was a very safe structure against a earthquake or a dynamic load. It can be said that most important factors in the stability of the geosynthetics reinforced wall are the horizontal length of reinforcement and the vertical distance between two reinforcements. That is to say, as the length of reinforcement is longer, the structure is more stable and as the vertical distance between two reinforcements is shorter, it is more stable. In this study, in order to get the critical condition with a safety rate of 1, various kinds of model tests about geosynthetics reinforced wall has been performed. Photos by B-shutter method has been taken during tests and from photos, which show us the failure state, the critical condition about failure has been conformed. Accordingly the equation, which says the limit of stability in geosynthetics reinforced wall., has been proposed.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2011년도 춘계학술대회 논문집
• /
• pp.1074-1079
• /
• 2011

This paper describes the influence on the nonlinear critical speed results of a specific railway vehicle depending on various constraint conditions. In the roller-rig tests, proper constraints are inevitable to safely hold the test vehicles. Particularly, the test results using KRRI roller-rig are more sensitive to constraint conditions because it is a kind of semi-full car type. In this study, nonlinear critical speed of specific vehicle with regards to several constraint cases were predicted by computational analysis and these results were compared to find the suitable constraint conditions. And also the deviation of semi-full car model from actual full car model was investigated. According to the bifurcation analysis, the nonlinear critical speed are dependent with the constraint condition and car-body yaw motion should be free to achieve more accurate results. And the difference between semi-full and full car model was so small that KRRI's semi-full car model are valid as long as the stability is concerned.

• Korean Journal of Mathematics
• /
• 제16권1호
• /
• pp.41-49
• /
• 2008

We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition $$u_{tt}-u_{xx}=au+b{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha-1}{\upsilon}_+^{\beta}+s{\phi}_{00}+f,\\{\upsilon}_{tt}-{\upsilon}_{xx}=cu+d{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha}{\upsilon}_+^{{\beta}-1}+t{\phi}_{00}+g,$$ where ${\alpha},{\beta}>1$ are real constants, $u_+={\max}\{u,0\},\;s,\;t{\in}R,\;{\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator and f, g are ${\pi}$-periodic, even in x and t and bounded functions.