• Honam Mathematical Journal
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• v.26 no.4
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• pp.589-608
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• 2004

We investigate the multiplicity of the periodic solutions of the nonlinear wave equation with jumping nonlinearity. By category theory we prove that the jumping problem has at least 2k+1 solutions for the positive source term.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.609-622
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• 1997

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $-\frac{2}{\pi}, \frac{2}{\pi}$ and periodic condition on the varible t, $Lu + bu^+ -au^- = f(x, t)$, when the jumping nonlinearity crosses the first positive eigenvalue.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.7
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• pp.699-709
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• 2009

In this paper, the nonlinear dynamics and the stability of nanopipes conveying fluid and modelled as a thin-walled beam is investigated. Effects of boundary conditions, geometric nonlinearity, non-classical transverse shear and rotary inertia are incorporated in this study. The governing equations and the three different boundary conditions are derived through Hamilton's principle. Numerical analysis is performed by using extend Galerkin method which enables us to obtain more exact solutions compared with conventional Galerkin method. Variations of critical flow velocity for different boundary conditions of carbon nanopipes are investigated and compared with linear case.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.11a
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• pp.85-89
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• 1997

A microstructure of realistic ZnO varistor was constructed by Voronoi network and studied cia computer simulation. The grain size and standard deviation was calculated with new method and have good agreement with experimental data. In this network, the grain boundary conditions of three different type are randomly distributed. The three electrical boundary conditions . (1) type A junctions (high nonlinearity); (2) type B junctions (low nonlinearity); (3) type C junctions (linear with low-resistivity) are fitted from the experimental measurement. The electrical properties were studied by varying the boundary type concentration and the disorder parameter d. The shape of I-V characteristic curve of the network is affected by the type concentration and the disorder parameter has an effect on the double inflected region.

• Smart Structures and Systems
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• v.22 no.6
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• pp.711-725
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• 2018

Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Hence, it is highly desirable to detect and characterize the nonlinearity present in the system in order to assess the true behaviour of the structural system. Further, these identified nonlinear features can be effectively used for damage diagnosis during structural health monitoring. In this paper, we focus on the detection of the nonlinearity present in the system by confining our discussion to only a few selective time-frequency analysis and multivariate analysis based techniques. Both damage induced nonlinearity and inherent structural nonlinearity in healthy systems are considered. The strengths and weakness of various techniques for nonlinear detection are investigated through numerically simulated two different classes of nonlinear problems. These numerical results are complemented with the experimental data to demonstrate its suitability to the practical problems.

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.47-57
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• 1989

• Journal for History of Mathematics
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• v.16 no.4
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• pp.107-115
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• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.