• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.723-738
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• 2015

In this paper, the prescribed mean curvature Rayleigh p-Laplacian equation with a deviating argument

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.333-343
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• 2010

The asymptotic behavior of solutions of higher order differential equations with deviating argument $$(py^{(n-1)}(t))'\;+\;\sum\limits_{i=1}^{n-1}ci(t)y^{(i-1)}(t)\;=\;f\[t,\;y(t),\;y'(t),\;{\ldots},\;y^{(n-1)}(t),\;y(\phi(t)),\;y'(\phi(t)),\;{\ldots},\;y^{(n-1)}\;(\phi(t))\]\;\;\;\;(1)$$ $t\;{\in}\;[0,\;\infty)$ is studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1) have some asymptotic behavior.

• 대한수학회지
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• 제44권3호
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• pp.673-682
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• 2007

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Rayleigh equation with a deviating argument of the form $x'+f(x'(t))+g(t,\;x(t-\tau(t)))=p(t)$.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.27-34
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• 2013

In this paper, we consider the Duffing type p-Laplacian equation with multiple deviating arguments of the form $$({\varphi}_p(x^{\prime}(t)))^{\prime}+Cx^{\prime}(t)+go(t,x(t))+\sum_{k=1}^ngk(t,x(t-{\tau}_k(t)))=e(t)$$. By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation. Moreover, an example is given to illustrate the effectiveness of our results.

• 대한수학회보
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• 제52권1호
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• pp.159-172
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• 2015

This paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• 철학연구
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• 제144권
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• pp.235-256
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• 2017

본 논문은 라이프니츠와 클라크 간의 공간의 본질에 대한 논쟁과 이를 바탕으로 한 최근 형이상학과 과학철학의 논쟁을 고찰한다. 공간의 본질에 대한 논의는 존재론적 위상에 대한 논쟁으로, 실체론(substantivalism)과 관계론(relationism)의 두 축을 중심으로 진행된다. 클라크에 의해 대변되는 실체론자들은 공간이 물체와 같이 그 자체적으로 존재하는 실체(substance)임을 주장한다. 반면, 라이프니츠를 위시한 관계론자들은 공간의 독립적인 실체성을 부정하고 공간이 물질들 사이의 관계(relation)로 환원될 수 있다고 주장한다. 라이프니츠는 식별불가능자 간의 동일성 원리와 충족이유율을 이용하여 실체론의 주장을 비판하는 논변을 제시한다. 이어만과 노턴에 의해 제시된 홀 논변은 고전적인 라이프니츠의 논변을 현대적인 문맥에서 계승하여 재구성한다. 본 논문은 이들 논변의 형이상학적 측면을 고려한다. 이를 통해 공간의 존재론에 대한 논의가 형이상학적 논쟁에 머무르지 않고 운동을 이해하는 역학 이론의 개념적 기초를 이루고 있음을 부각한다.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.