• 한국소음진동공학회논문집
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• 제15권12호
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• pp.1355-1360
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• 2005

Periodic structures can be applied as a MEMS(micro-electro-mechanical system) sensor or actuator due to low energy loss and wideband frequency response. The dynamic behavior of a mistuned periodic structure Is dramatically changed from that of a perfectly tuned periodic structure. The effects of mistuning, coupling stiffness, and driving point on the forced vibration responses of a simple periodic structure ate investigate4 through numerical simulations. On the basis of that, one can design effective and reliable MEMS components using periodic structures.

• 충청수학회지
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• 제15권2호
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• pp.47-56
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• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.471-489
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• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• 대한수학회논문집
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• 제25권2호
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• pp.263-271
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• 2010

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

• 한국정밀공학회지
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• 제12권1호
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• pp.123-131
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• 1995

다주파수 입력을 갖는 강한 비선형 시스템의 유사주기 (quasi-periodic) 해를 해석하기 위하여 개선된 고정 점법(FPA:Fixed Point Alogrithm)을 개발하였다. 안정성 및 천이 특성을 판별하기 위하여 사용되어지는 Floquest 지수인 해석적 자코비언을 구하기 위하여 Poincare 맵상에서 이산 적분법을 새로이 고안, 사용하였다. 본 방법의 우수성을 입증하기 위하여 2개의 주파수 입력을 갖는 선형 시스템과 비선형 시스템을 예로 사용하였다. 본 방법을 이용하여 비선형 시스템에서 발생한 복잡한 chaos 현상을 체계적으로 해석하였다.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.1029-1038
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• 2000

In this paper, we show that if x is a positively Lyapunov stable point of an expansive homeomorphism with the pseudo-orbit-tracing-property, then x is a periodic point or its positive limit set consists of only one periodic orbit, and their periods are predictable. We give a necessary and sufficient condition that a basic set is to be a sink or source. Also, we consider some dynamical properties of basic sets.

• Korean Journal of Mathematics
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• 제21권1호
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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.

• 대한수학회보
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• 제27권2호
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• pp.127-131
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• 1990

Let f:R.rarw.R be a continuous function on the real line R, and denote the n-th iterate of f by f$^{n}$ :f$^{1}$=f and f$^{n}$ =f.f$^{n-1}$ for n>1. A point x.mem.R is a periodic point of f of period k>0 if f$^{k}$ (x)=x but f$^{i}$ (x).neq.x for all 01, then it must also have a fixed point, by the intermediate Theorem. Also the question has an intriguing answer which was found by ths Russian mathematician Sharkovky [6] in 1964.

• 호남수학학술지
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• 제40권1호
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• pp.1-11
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• 2018

We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].

• 충청수학회지
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• 제31권1호
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• pp.13-27
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• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.