• Title, Summary, Keyword: upper semicontinuity

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SADDLE POINTS OF VECTOR-vALUED FUNCTIONS IN TOPOLOGICAL VECTOR SPACES

  • Kim, In-Sook
    • Journal of the Korean Mathematical Society
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    • v.37 no.5
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    • pp.849-856
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    • 2000
  • We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

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UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS GENERALIZED 2D PARABOLIC EQUATIONS

  • PARK, JONG YEOUL;PARK, SUN-HYE
    • Journal of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1149-1159
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    • 2015
  • This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITY WITH LOCAL NON-POSITIVITY

  • Lee, Byung-Soo
    • Communications of the Korean Mathematical Society
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    • v.24 no.3
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    • pp.425-432
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    • 2009
  • This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITIES WITH FQ-COMPLEMENTARITY PROBLEMS

  • Lee, Byung-Soo
    • Honam Mathematical Journal
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    • v.31 no.2
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    • pp.247-258
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    • 2009
  • This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].

UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON ℝN

  • Anh, Cung The;Nguyen, Duong Toan
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1299-1324
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    • 2014
  • We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

A NEW MINIMUM THEOREM AND ITS APPLICATIONS

  • Kim, Won-Kyu;Rim, Dong-Il;Im, Sung-Mo
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.932-944
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    • 1998
  • In this paper we first prove a new minimum theorem using the upper semicontinuity of minimizing functions, which is comparable to Berge's theorem. Next, as applications, we shall prove the existence of equilibrium in generalized games and the existence theorem of zeros.

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A SHORT REMARK ON CONTROL SYSTEMS

  • Chu, Hahng-Yun;Ku, Se-Hyun;Yoo, Seung Ki
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.165-170
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    • 2016
  • Souza and Tozatti [7] introduce the notions of prolongations and prolongational limit sets on control systems. In this article, we prove the upper semicontinuity of first positive prolongations and first positive prolongational limit sets on control systems.

PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

  • Fridman, Buma L.;Ma, Daowei
    • Journal of the Korean Mathematical Society
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    • v.40 no.3
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    • pp.487-501
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    • 2003
  • The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in \mathbb{C}^n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in \mathbb{C}^n does not exceed n.

ON THE HIGHER ORDER KOBAYASHI METRICS

  • KIM, JONG JIN;HWANG, IN GYU;KIM, JEONG GYUN;LEE, JEONG SEUNG
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.549-557
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    • 2004
  • In this paper, we prove the product property and the existence of an extremal analytic disc relative to the higher order Kobayashi metric. Also by making use of the upper semicontinuity of the higher order Kobayashi metric, we introduce a pseudodistance and investigate some properties of that pseudodistance related to the usual Kobayashi metric.

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