• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.835-847
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• 2000

We investigate various ${\Phi}$(t)-stability of comparison differential equations and we obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f(t, x).

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.551-560
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• 2007

We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.

• 전기의세계
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• v.29 no.1
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• pp.58-64
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• 1980

In this paper, this objective is to obtain the mathematical model which describes the dynamic characteristics of variable reluctance(VR) step motor, the most important and most widely used motor in practice. In the development of the mathematical model for VR step motor, first the general nonlinear dynamic equations which describe the N-phase VR step motor are derived. These general equations are then applied to the multiple-step type of VR step motor in case, for simplicity, maynetic saturation and core lossess in the iron are neglected. These nonlinear dynamic equations are numerically analysed by the computer simulation, through which the performance characteristics of a step motor undertest are investigated under the various operating conditions.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.125-138
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• 2003

Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $\Delta$(a(n)$\Delta$(x(n) - px(n-$\tau$))) + f(n, x($\sigma$(n))) = 0 using these inequalities we obtain some oscillation criteria for the above equation.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.436-439
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• 1992

A tubular reactor model represented by partial differential equations was studied as one of nonlinear distributed parameter optimal control problems. An optimal control theory in the form of maximum principles based on nonlinear integral equations was used to develop an algorithm to solve the problem.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.851-864
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• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.1-4
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• 2003

This paper we study the existence of a global solution for the nonlinear fuzzy differential equations in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . .

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.231-243
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• 2015

We suggest and analyze a family of multi-step iterative methods for solving nonlinear equations using the decomposition technique mainly due to Rafiq et al. [13].

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.726-730
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations in E$^{2}$$_{N}$.