• Title/Summary/Keyword: Strongly indefinite functional

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PERIODIC SOLUTIONS FOR THE NONLINEAR HAMILTONIAN SYSTEMS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.17 no.3
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    • pp.331-340
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    • 2009
  • We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

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SOLVABILITY FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun;Choi, Q-Heung
    • Honam Mathematical Journal
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    • v.31 no.1
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    • pp.75-85
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    • 2009
  • We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

MULTIPLICITY RESULTS AND THE M-PAIRS OF TORUS-SPHERE VARIATIONAL LINKS OF THE STRONGLY INDEFINITE FUNCTIONAL

  • Jung, Tack-Sun;Choi, Q-Heung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.4
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    • pp.239-247
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    • 2008
  • Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

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THE NUMBER OF THE CRITICAL POINTS OF THE STRONGLY INDEFINITE FUNCTIONAL WITH ONE PAIR OF THE TORUS-SPHERE VARIATIONAL LINKING SUBLEVELS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.16 no.4
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    • pp.527-535
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    • 2008
  • Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

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VARIATIONAL APPROACH AND THE NUMBER OF THE NONTRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF THE SYSTEM OF THE NONTRIVIAL SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun;Choi, Q-Heung
    • The Pure and Applied Mathematics
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    • v.16 no.2
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    • pp.199-212
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    • 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.

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Topic Continuity in Korea Narrative (한국 설화문에서의 화제표현의 연속성)

  • Hi-JaChong
    • Korean Journal of Cognitive Science
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    • v.2 no.2
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    • pp.405-428
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    • 1990
  • Language has a social function to communicate information. Linguists have gradually paid their attention to the function of language since the nineteen sixties, especially to the relationship of form, meaning and the function. The relationship could be more clearly grasped through disciyrse-based analysis than through sentence-based analysis. Many researches were centered on the discourse functional notion of topic. In the early 1970's the subject was defined as the grammatiocalized topic the topic as a discrete single constituent of the clause. In the late 1970's several lingusts including Givon suggerted that the topic was not an atomic, disctete entity, and that the clause could have more than one topic. The purpose of the present study is, following Givon, to study grammatical coding devices of topic and to measure the relative topic continuity/discontinuity of participant argu, ents in Korean narratives. By so doing, I would like to shed some light on effective ways of communicating information. The grammatical coding devices analyzed are the following eight structures: zero-anaphora, personal pronous, demonstrative pronouns, names, noun phrases following demonstratives, noun phrases following possessives, definite noun phrases and indefinite referentials. The narrative studied for the count was taken from the KoreanCIA chief's Testiomny:Revolution and Idol by Hyung Wook Kim. It was chosen because it was assumed that Kim's purpose in the novel was to tell a true story, which would not distort the natural use of language for literary effect. The measures taken in the analysis wre those of 'lookback', 'persistence', ambiguity'. The first of these, 'lookback', is a measure of the size of gap between the previous occurrence of a referent and its current occurence in the clause. The meausure of persistence, which is a measure of the speaker's topocal intent, reflects the topic's importance in the discourse. The third measure is a measure of ambiguity. This is necessary for assessing the disruptive effects that other topics within five previous clauses may have on topic identification. The more other topics are present within five previous clauses, the more difficult is the task of correct identification of a topic. The results of the present study show that the humanness of entities is the most powerful factior in topic continutiy in narrative discourse. The semantic roles of human arguments in narrative discourse tend to be agents or experiences. Since agents and experiences have high topicality in discourse, human entities clearly become clausal or discoursal topics. The results also show that the grammatical devices signal varying degrees of topic continuity discontinuity in continuous discourse. The more continuous a topic argument is, the less it is coded. For example, personal pronouns have the most continutiy and indefinite referentials have the least continutiy. The study strongly shows that topic continuity discontinutiy is controlled not only by grammatical devices available in the language but by socio-cultural factors and writer's intentions.