• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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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].

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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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.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1257-1269
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• 2013

Using the three critical points theorem by B. Ricceri [23], we obtain a multiplicity result for a class of nonlocal problems in Orlicz-Sobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1541-1547
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• 2011

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1235-1250
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• 2010

In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.

• Journal of the Korean Professional Engineers Association
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• v.33 no.4
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• pp.44-47
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• 2000

Recently number of reinstrumentation projects in the process plants has grown to meet the needs to modernize or upgrade the exsisting control systems in a bid to boost productivity and quality. Design, installation and start-up of these process automation systems can be successful and trouble-free only if decision points are addressed properly. The critical decision points are encountered from tile design through the start-up phases of implementing a modernization project and discussed extensively here on a practical basis. Key points are ;to assign a project manager out of the plant instrument engineers for him to organize and lead a project team. ;to follow three critical steps in designing and implementing. :to think ahead of the critical steps and to induce a positive cooperation from all level of participants in the effort to prevent possible schedule delays.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.407-414
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• 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 English Language & Literature
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• v.64 no.1
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• pp.25-37
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• 2018

The turning point is one of the more evocative concepts in the critic's arsenal, as it is equally suited to the evaluation and analysis of a given moment in one's day as to those of a historical event. But how does one recognize a turning point? As we find ourselves always "in the middest," both spatially and temporally, we inhabit sites that may be points at which many things may be seen to turn. Indeed, it is usually only possible to identify a turning point, as it were, from a distance, from the remove of space and time which allows for a sense of recognition, based in part on original context and in part of perceived effects. In this article, Robert T. Tally Jr. argues that the apprehension and interpretation of a turning point involves a fundamentally critical activity. Examining three models by which to understand the concept of the turning point-the swerve, the trope, and peripety (or the dialectical reversal)-Tally demonstrates how each represents a different way of seeing the turning point and its effects. Thus, the swerve is associated with a point of departure for a critical project; the trope is connected to continuous and sustained critical activity in the moment, and peripety enables a retrospective vision that, in turn, inform future research. Tally argues for the significance of the turning point in literary and cultural theory, and concludes that the identification, analysis, and interpretation of turning points is crucial to the project of criticism today.

• Journal of Power System Engineering
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• v.10 no.4
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• pp.119-126
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• 2006

Gerotor hydraulic motor is widely used in hydraulic systems due to its low speed, high torque output and compactness in rotational direct driving of a heavy weight. Gerotor is a Planar mechanism consisted of a pair of rotor and circular teeth of stator assembly which forms a closed space, so called a chamber. The motion of rotor relative to the circular tooth is produced by the pressure difference of hydraulic operating fluid between the adjacent chamber. As all active contact points of rotor and circular teeth are subjected to very high sliding friction, a reduction in the performance of the gerotor hydraulic motor can not be avoided. Therefore, the core design parameters of gerotor profile used in hydraulic motors is to minimize a friction force by high contact stresses. The analytical design method of gerotor profile, based on envelope of a family of curves, is proposed. In this study, the influence of the tip clearances on three critical contact points between rotor and circular teeth of stator assembly has been explored by experimental data in this paper. At the same time a improvement method to reduce the friction force is proposed and the tip clearances on three critical points for getting an optimum gerotor profile are also analyzed.