• Korean Journal of Mathematics
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• 제17권2호
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.1-13
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• 2016

This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.

• 대한수학회지
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• 제34권2호
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• pp.407-426
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• 1997

We consider a system of perturbed linear differential equation x' =A(t)x + f(t,x) and obtain conditions to ensure the strong-equiasymptotic stability of the zero solution.

• 천문학논총
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• 제16권1호
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• pp.7-10
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• 2001

In the framework of the C-gauge condition for the perturbed variables and the linear approximation for the anisotropy of the spacetime, we studied the formulae for the Sachs-Wolfe effect in dust filled and perturbed Bianchi type I universe model. The results were compared with those of the flat Friedmann model.

• 충청수학회지
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• 제29권1호
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• pp.1-11
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• 2016

This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• 충청수학회지
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• 제29권2호
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.

• Communications for Statistical Applications and Methods
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• 제15권4호
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• pp.483-496
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• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권3호
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• pp.201-215
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• 2018

In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

• 충청수학회지
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• 제29권3호
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• pp.429-442
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• 2016

In this paper we show that the solutions to the perturbed differential system $$y^{\prime}=f(t,y)+{\int}_{to}^{t}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic behavior by imposing conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system y' = f(t, y).