• Proceedings of the KIEE Conference
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• 2006.07a
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• pp.8-9
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• 2006

This paper presents a new methodology to calculate an optimal solution of equilibrium to power system differential algebraic equations. It employs a nonlinear interior point method for solving the optimization formulation, which includes dynamic equations representing two-axis synchronous generator models with AVR and speed governing control, algebraic equations, and steady-state nonlinear loads. Equilibrium optimization (EOPT) is useful for diverse purposes in power system analysis and control with consideration of the system frequency constraint.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.17-28
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• 2017

A combined form of the modified Laplace Adomian decomposition method (LADM) is developed for the analytic treatment of the nonlinear Volterra-Fredholm integro differential equations. This method is effectively used to handle nonlinear integro differential equations of the first and the second kind. Finally, some examples will be examined to support the proposed analysis.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.313-329
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• 2020

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.243-253
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• 2003

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.1-10
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• 2012

Let ${\Omega}$ be a bounded subset of $\mathbb{R}^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.675-681
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• 2018

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1011-1020
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• 2021

In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.227-238
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• 2017

The existence of solutions for nonlinear elliptic partial differential equations with general flux and damping terms is investigated.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.489-501
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• 2003

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.