• Title/Summary/Keyword: Critical point

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ELLIPTIC BOUNDARY VALUE PROBLEM WITH TWO SINGULARITIES

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.26 no.1
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    • pp.9-21
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    • 2018
  • We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

BIFURCATION PROBLEM FOR THE SUPERLINEAR ELLIPTIC OPERATOR

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.20 no.3
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    • pp.333-341
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    • 2012
  • We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

BOUNDED WEAK SOLUTION FOR THE HAMILTONIAN SYSTEM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.21 no.1
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    • pp.81-90
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    • 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.

DIRICHLET BOUNDARY VALUE PROBLEM FOR A CLASS OF THE ELLIPTIC SYSTEM

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.707-720
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    • 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.

A Study on the Analysis and Control of Voltage Stability (전압안정성 분석 및 제어에 관한 연구)

  • 장수형;김규호;유석구
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.43 no.6
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    • pp.869-876
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    • 1994
  • This paper presents an efficient method to calculate voltage collapse point and to avoid voltage instability. To evaluate voltage stability in power systems, it is necessary to get critical loading points. For this purpose, this paper uses linear programming to calculate efficiently voltage collapse point. Also, if index value becomes larger than given threshold value, voltage stability is improved by compensation of reactive power at selected bus. This algorithm is verified by simulation on the IEEE 14-bus sample system.

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TOPOLOGICAL ASPECTS OF THE THREE DIMENSIONAL CRITICAL POINT EQUATION

  • CHANG, JEONGWOOK
    • Honam Mathematical Journal
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    • v.27 no.3
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    • pp.477-485
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    • 2005
  • Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

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EXISTENCE OF SIX SOLUTIONS OF THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tack-Sun;Choi, Q-Heung
    • Honam Mathematical Journal
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    • v.30 no.3
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    • pp.443-468
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    • 2008
  • We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

EXISTENCE THEOREMS OF BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER NONLINEAR DISCRETE SYSTEMS

  • YANG, LIANWU
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.399-410
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    • 2019
  • In the manuscript, we concern with the existence of solutions of boundary value problems for fourth order nonlinear discrete systems. Some criteria for the existence of at least one nontrivial solution of the problem are obtained. The proof is mainly based upon the variational method and critical point theory. An example is presented to illustrate the main result.

A Theoretical Investigation of Nonlinear Chemical Reactions Near the Critical Point in the Presence of Diffusion

  • Shin, Seok-Min;Shin, Kook-Joe
    • Bulletin of the Korean Chemical Society
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    • v.7 no.4
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    • pp.283-288
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    • 1986
  • A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.