• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.635-643
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• 2002

The asymptotic behaviour of the solutions of initial - boundary value problem for a class of nonlinear parabolic differential - functional equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.39-47
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• 2003

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7］are generalized and improved.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.81-88
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• 2009

In this paper, we investigate h-stability for the nonlinear Volterra integro-differential equations and the functional integro-differential equations.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.105-107
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• 1991

A chemical process model represented by partial differential equations was studied as one of nonlinear distributed parameter control problems. Using an optimal control theory in the form of maximum principles based on nonlinear integral equations, an algorithm to solve the problem was developed and coded into a computer program.

• 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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.683-699
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• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.883-892
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• 2010

This paper is concerned with oscillation property of solutions of a class of second order nonlinear differential equations with perturbation. Four new theorems of oscillation property are established. These results develop and generalize the known results. Among these theorems, two theorems in the front develop the results by Yan J(Proc Amer Math Soc, 1986, 98: 276-282), and the last two theorems in this paper are completely new for the second order linear differential equations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.621-626
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• 1985

Unsteady groundwater flow in a three-layer unconfined aquifer has been studied theoretically and experimentally. Two different methods have been used in solving the governing equations of the flow, the nonlinear partial differential equations; (1) The governing equations are linearized for each layer and approximate solutions are obtained. (2) The governing equations are transformed to nonlinear ordinary differential equations, which are solved numerically by Runge-Kutta procedure. Fine, middle sized and coarse sands are used in the experiments. It is found that the solutions from the method(2) ( the reduction of partial differential equations to ordinary differential equations) give better agreement with the experimental results than the solution from the method(1).

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1069-1088
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• 2015

In this paper, some basic results concerning the existence, strict and nonstrict inequalities and existence of the maximal and minimal solutions are proved for a hybrid causal differential equation. Our results generalize some basic results of Leela and Laksh-mikantham [13] and Dhage and Lakshmikantham [10] respectively for the nonlinear first order classical and hybrid differential equations.