• Korean Journal of Mathematics
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• 제19권1호
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• pp.101-109
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• 2011

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.467-481
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• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.51-64
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• 1996

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.

• 호남수학학술지
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• 제29권1호
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• pp.19-40
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• 2007

Let L be the differential operator, Lu = $u_{tt}+u_{xxxx}$. We consider nonlinear beam equations, Lu + $bu^+$ = j, in H, where H is the Hilbert space spanned by eigenfunctions of L. We reveal the existence of multiple solutions of the nonlinear beam problems by critical point theorems.

• 충청수학회지
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• 제21권1호
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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.

• 충청수학회지
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• 제22권2호
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• pp.251-259
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• 2009

We investigate the multiple solutions for the nonlinear parabolic boundary value problem with jumping nonlinearity crossing two eigenvalues. We show the existence of at least four nontrivial periodic solutions for the parabolic boundary value problem. We restrict ourselves to the real Hilbert space and obtain this result by the geometry of the mapping.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.435-440
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• 2000

It is shown, in nonlinear two-degree-of freedom system, that the bifurcating modes are created by the stability changes of normal modes. There are four types of stability criterion, each of which gives rise to a distinct functional form of bifurcating modes; the bifurcating mode is born in the form of eigenfunction through which the stability is changed. Then a procedure is formulated to compute the bifurcating mode by the method of harmonic balance. Application of bifurcating mode to forced vibrations is introduced.

• 한국정밀공학회지
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• 제6권3호
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• pp.100-108
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• 1989

The frequency equation and numerical process of natural frequencies for several boundary conditions of L-type folded plate given to the different thickness and lenth are derived by using Rayleigh-Ritz method in this study. Those natural frequencies are attaind by choosing the proper eigenfunction for boundary conditions of x-direction and y-direfction beams, by considering the convergence of numerical results.

• Korean Journal of Mathematics
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• 제5권1호
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• pp.29-33
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• 1997

In this paper we investigate the existence of positive solutions of a nonlinear biharmonic equation under Dirichlet boundary condition in a bounded open set ${\Omega}$ in $\mathbf{R}^n$, i.e., $${\Delta}^2u+c{\Delta}u=bu^{+}+s\;in\;{\Omega},\\u=0,\;{\Delta}u=0\;on\;{\partial}{\Omega}$$.

• 한국해안해양공학회지
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• 제14권3호
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• pp.183-191
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• 2002

해수교환이 우수하고, 조차에 따라 상·하로 자유롭게 운동하며, 연약지반과 대수심역에도 설치될 수 있다는 것을 일반적인 부방파제의 주요한 특징으로 들 수 있다. 본 연구는 말뚝계류된 부방파제에 의한 3차원파랑제어와 동적인 거동을 경계적분법과 고유함수전개법을 병용하는 수치해석법으로부터 논의한다. 여기서, 말뚝계류시스템은 연직운동만이 허용되고 다른 운동성분들은 모두 구속되며, 체인계류시스템보다도 파랑에너지의 흡수가 많은 것으로 알려져 있다. 본 연구에서는 말뚝계류에 있어서 말뚝과 본체인 폰툰과의 사이에 작용하는 마찰력과 같은 저항력은 고려되지 않는다. 수치해석결과에 따르면 부방파제의 홀수와 폭의 변화는 파랑제어에 큰 영향을 미치고, 입사파의 주기가 길면 부방파제를 통한 전달파가 크다는 것을 알 수 있다. 그리고, 부방파제의 연직운동은 단주기파에서 크게 나타난다.