• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.671-684
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• 2019

In this paper, we propose a new interior point method for solving nonlinear complementarity problems. In this method, we use a new profitable searching direction and instead of using the logarithmic quadratic term, we use a square root quadratic term. We prove the global convergence of the proposed method under the assumption that F is monotone. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

• East Asian mathematical journal
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• v.19 no.2
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• pp.173-187
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• 2003

We study decay estimates of the energy for the nonlinear wave equation in the whole space. We note that the method of proof is based on the multiplier technique and on the unique continuation, and no geometrical condition is imposed on the boundary.

• East Asian mathematical journal
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• v.33 no.3
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• pp.295-308
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• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.985-999
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• 2011

A new filled function method is presented in this paper to solve box-constrained nonlinear integer programming problems. It is shown that for a given non-global local minimizer, a better local minimizer can be obtained by local search starting from an improved initial point which is obtained by locally solving a box-constrained integer programming problem. Several illustrative numerical examples are reported to show the efficiency of the present method.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.319-330
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• 2002

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.411-421
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• 2015

This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1179-1192
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• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.609-619
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• 2005

We are concerned with the multiplicity of solutions of the nonlinear elliptic equation with Dirichlet boundary condition. We reveal the existence of m solutions of the nonlinear elliptic equation by a critical point theory, under some condition.