• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.569-578
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• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.87-96
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• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1109-1118
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• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• Journal of Industrial Technology
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• v.31 no.A
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• pp.21-25
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• 2011

A comparison of temperature distributions along the fin length coordinate between two different fin tip boundary conditions for a circular pin fin is made by using the one-dimensional analytic method. One tip boundary condition is the actual fin tip boundary condition and fin tip temperature is arbitrarily given for another fin tip boundary condition. The value of the fin base temperature is depend on the fin base thickness and fin radius. One of the results shows that the temperature distribution along the fin length coordinate for the actual fin tip boundary condition and that for the arbitrarily given fin tip temperature are the same if the arbitrarily given fin tip temperature and the fin tip temperature for the actual fin tip boundary condition are the same.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.209-220
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• 2007

In this paper, the existence and multiplicity of solutions of three-point p-Laplacian boundary value problems at resonance with one-sided Nagumo condition are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2684-2689
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• 2007

Non-equilibrium first order extrapolation boundary condition proposed by Guo et $al.^{(9)}$ proposed has a good application for complex geometries, a second order accuracy and a treatment on non-slip wall boundary condition easily. However it has a lack of the numerical stability from high Reynolds number. Guo et $al.^{(9)}$ substituted the density value of adjacent nodes for the density of boundary nodes. This procedure causes the numerical instability on the boundary. In this paper, we derived a procedure of density extrapolation and compared to previous results.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.10a
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• pp.99-103
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• 2003

An analysis of the flow within supersonic turbine cascades is necessary to design and manufacture turbo-pump system. Because of the differences between the specified inlet boundary value and the computed inlet value caused by the far field inlet boundary condition, the computations at desired inlet conditions can not be achieved. So, this paper studied the problem occurred when far field inlet conditions were specified as inlet boundary conditions. And the numerical analyses using Fine Turbo, CFD Program, has been performed and compared with those of experiments when a converging-diverging nozzle or a linear nozzle was located in front of cascades instead of the far field inlet condition.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.