• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.559-571
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• 2004

The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.83-88
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• 1996

In 1994 Z.Liang constructed an iterative method for the solution of nonlinear equations involving m-accretive operators in uniformly smooth Banach spaces. In this paper we apply the slight variants of Liang's iterative methods and generalize the results of Z.Liang. Moreover our proof is more simple than Liang's proof.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.7-14
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• 2010

In this paper, we construct some improvements of the Jarratt method for solving non-linear equations. A new sixth-order method are developed and numerical examples are given to support that the method obtained can compete with other sixth-order iterative methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.85-89
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• 2001

Hamiltonian modeling approach has been extensively adopted for rigid body dynamics whereas its usage for deforming flexible continuum dynamics has been limited. A set of Hamilton＇s equations for flexible body motion with finite deformation has been derived and applied for a nonlinear impact problem.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.347-356
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• 2007

In this paper, we shall consider a class of hyperbolic nonlinear differential equations with continuous deviating arguments. Some new sufficient conditions for oscillation of all solutions with two kinds of boundary conditions are obtained.

• Kyungpook Mathematical Journal
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• v.29 no.2
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• pp.141-147
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• 1989

The existence and uniqueness of solutions of nonlinear Volterra-Fred-holm integral equations of the more general type are investigated. The main tool employed in our analysis is the method of successive approximation based on the general idea of T.Wazewski.

• East Asian mathematical journal
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• v.39 no.1
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• pp.51-63
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• 2023

We establish the interior L^q regularity estimates for spatial gradient of weak solutions to nonlinear parabolic equations with the inhomogeneity which is given by the divergence and nondivergence data.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.299-312
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• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.689-700
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• 2005

In this paper we shall introduce the general idea, historical background and the reasons why we use it about the homotopy method for solving a system of nonlinear systems.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.165-174
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• 1996

Using the comparison principle and inequalities we obtain some results on boundedness and stabilities of solutions of the nonlinear functional differential equation $y^{\prime}=f(t,y)+g(t,y,Ty)$.