• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.201-215
• /
• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Kirchhoff-type equations $\[a+b\({\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx\)\][-{\Delta}u+V(x)u]=f(x,u)$, in ${\mathbb{R}}^N$. Under certain assumptions on V and f, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.407-414
• /
• 2020

In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.39-48
• /
• 2011

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian by the minimax methods in critical point theory.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.10
• /
• pp.1355-1364
• /
• 2001

Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder, where the Taylor's hypothesis does nut hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV for various planes of view. The convection velocities of the Karman and secondary vortices are evaluated from the trajectory of the vortex center. Then, saddle points are determined by applying the critical point theory. It is shown that the inclination angle of the secondary vortices agrees well with the previous experimental data. The flow fields in a moving frame of reference have several critical points and the mushroom-like structure appears in the streamline patterns of the secondary vortices. Since the distributions of fluctuating Reynolds stresses defined by triple decomposition are closely related with the existence of secondary vortices, the physical meaning of them is explained in conjunction with the vortex center and saddle point trajectories.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.669-684
• /
• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Proceedings of the KSME Conference
• /
• 2001.06b
• /
• pp.513-518
• /
• 2001

This research has been performed to estimate the hunting motion hysteresis of railway passenger cars. An old and a new car with almost same structure are chosen as analysis models. To solve effectively a set of simultaneous equations of motion strongly coupled with creep relations, shooting algorithm in which the nonlinear relations are regarded as a two-point boundary value problem is adopted. The bifurcation theory is applied to the dynamic analysis to distinguish differences between linear and nonlinear critical speeds by variation of parameters. It is found that there are some factors and their operation area to make nonlinear critical speed respond to them more sensitivity than linear critical speed. Full-scale roller rig tests are carried out for the validation of the numerical results. Finally, it is concluded that the wear of wheel profile and the stiffness discontinuities of wheelset suspension caused by deterioration have to be considered in the analysis to predict hysteresis of critical speed precisely.

• Journal of Advanced Marine Engineering and Technology
• /
• v.38 no.10
• /
• pp.1263-1268
• /
• 2014

In this study, the variations of swirl center according to evaluating position have been investigated in a steady flow bench of SI engine. For the experiments, two engine heads with different intake valve angles ($11^{\circ}$ and $26^{\circ}$) were tested in the flow bench by varying the evaluating position (1.75~6.0B) and valve lift (2~10 mm). Particle image velocimetry was used to measure the velocity field inside the engine cylinder. The swirl center position is found with a critical point theory and the intensity of turbulence is calculated from PIV velocity data. The results show that the center of swirl is located closer to the center of cylinder and turbulence intensity is lower, when the intake valve angle is the smaller. It is conventional to evaluate the swirl ratio at 1.75B position in the steady flow bench of SI engine. At this position, however, the distance of swirl center from the cylinder center scatters significantly for the variation of valve lift, and the turbulence intensity is much stronger regardless of the valve angle. Thus, to estimate the flow at the end of compression stroke in a real engine from the data in the steady flow experiments, the evaluation position should be moved further downstream more than 4.5B.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.51-62
• /
• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Journal of the Korean Society of Safety
• /
• v.7 no.4
• /
• pp.45-53
• /
• 1992

Sponataneous ignition characteristics for granulated activated carbon were observed by performing experiments at constant ambient temperature and varying the ambient temperature sinusoidally. In case of varying the ambient temperature sinusoidally, the amplitudes of temperature were 5$^{\circ}C$, 1$0^{\circ}C$ and 15$^{\circ}C$ respectively, and the period in each amplitude was varied at an interval of 30minutes from zero to 3hours. As the results of experiments at a constant ambient temperature, the critical spontaneous ignition temperature of the sample decreased as the sample vessel size increased. Apparent activation energy of the sample calculated from the Frank-Kamenetskii's thermal Ignition theory was 38.82［kca1/mo1］ In case of varying the ambient temperature sinusoidally, the critical spontaneous ignition tempera-ture was lower than that at the constant ambient temperature, and the minimum critical spontaneous ignition temperature decreased with the amplitude of heating sinusoidal curve. At the same amplitude, the critical spontaneous ignition temperature decreased until it reached the minimum point and then in-creased as the period increased.

• Industrial Engineering and Management Systems
• /
• v.15 no.4
• /
• pp.385-395
• /
• 2016

Game theory is a powerful tool for analyzing the Supply chain (SC) with different conflicting elements. Among them, the Stackelberg game is the one in which a player as leader has more power than the other ones as followers. Since in many SC systems one element has, in essence, more power than the others; the Stackelberg game has found many applications in SC studies. In this paper, we apply the Stackelberg game-theoretic approach and the corresponding equilibrium point to formulate and analyze a two echelon VMI SC. Comprehensive computational results on an experimental case are conducted to numerically analyze the performance of VMI system against three groups of critical parameters. Moreover, a critical comparison demonstrates the poorer performance of decentralized VMI system than centralized one. This naturally necessitates designing proper contracts between VMI partners in order to more effectively implement the realistic decentralized system.