• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.740-745
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• 1988

New design methods for constructing nonlinear adaptive control system are considered. The proposed adaptive controllers are applicable to the case where the degree of the controlled process is unknown. It is shown that the degree of the controller is determined independently of the degree of the process. Several types of nonlinear functions are introduced to deal with uncertainties of the degree of the process. Finally, some simulation results show the effectiveness and simplicity of the proposed methods.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.368-373
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• 1998

This paper presents a GA-based fuzzy modelling scheme of nonlinear systems. The fuzzy model is a type of the Sugeno-Tagaki's fuzzy model whose consequence parts are described by a linear continuous dynamic equation as subsystem of a nonlinear system. The centers and width of the membership functions of the fuzzy sets defined over the input space and the orders and parameters of subsystems in the consequence parts are adjusted by a genetic algorithm. The effectiveness of the proposed method is verified

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.861-864
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• 1993

This research provides the results of a trial to generate the chaos by using nonlinear function constructed by fuzzy inference rules. The chaos generation function or chaotic behavior can be obtained by using Takagi-Sugeno fuzzy model with some constraint of the relationship of its parameters. Two examples are shown in this research. The first is simple example that construct of logistic image by fuzzy model. The second is more complicated one that provide the chaotic time series by non-linear autoregression based on fuzzy model. Simulated results are shown in these examples.

• Journal of the Korea Society for Simulation
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• v.10 no.3
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• pp.31-46
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• 2001

Repeated measurements on units under different conditions are common in biological and biomedical studies. In a number of growth and pharmacokinetic studies, the relationship between the response and the covariates is assumed to be nonlinear in some unknown parameters and the form remains the same for all units. Nonlinear random coefficient models are used to analyze such repeated measurement data. Extended least squares methods are proposed in the literature for estimating the parameters of the model. However, neither objective function has closed form expression in practice. This paper proposes Monte Carlo methods to estimate the objective functions and the corresponding estimators. A simulation study that compare various methods is included.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.145-164
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• 2011

In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].