• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1361-1370
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• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.

• KIEAE Journal
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• v.12 no.3
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• pp.41-46
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• 2012

The building envelope is important specially for saving energy consumption of residential buildings. but Apartment houses in Korea commonly have inside insulation system which have constantly arisen thermal bridges, the risk of heat loss, as a necessity. This study aims to evaluate integrated insulation performance according to the different shapes of external walls, adjacent to windows. The thermal performance analysis was carried out by Equivalent U-value and using the three-dimensional heat transfer computer simulation (TRISCO-RADCON), under nine different cases of comparing among three each of different bases(current standard model, 30percent energy saving model and 60percent energy saving model). The heating and the cooling load were also compared between two cases (standard U-value and Equivalent U-value) of three each of different bases, using the Building energy simulation which is based on DOE-2.1 analysis. As results, it turns out that if the Equivalent U-value is considered on the envelope analysis, the heat flow loss will be increasing more than the standard U-value, and if heat insulation property of the residential building reinforced rather than current, the rate of influences on the thermal bridges would be extremely expanded. In addition, it is shown that annual heating loads of the apartment house with applied Equivalent U-value substantially increased by more than 15 percent compared to those with the existing U-value, but annual cooling loads were negligibly affected.

• Architectural research
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• v.15 no.4
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• pp.201-206
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• 2013

Special attention is required for the design of windows due to their high thermal vulnerability. This paper examines the problems that might arise in the application of the u-value, by reflecting the changes in the u-value of the window, depending on the window-to-wall ratio obtained in an energy demand analysis. Research indicates that the u-value of a window increases with an increase in the difference between the u-values of the frames and the glass. Relative to the changes in the u-value of the windows, the energy demand varied from 1.3% to 9.3%. Windows with a g-value of 0.3 or 0.5 displayed a higher energy demand than windows with a g-value of 0.7. Therefore, when the difference between the performance of the glass and the frame is significant, especially when the g-value is small, a modified heat transmission coefficient should be applied to the window size during the evaluation of the building energy demand.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.79-87
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• 2009

This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian $({\phi}_p(u'))'(t)$ + f(t,u(t)) = 0, $t{\in}$ (0, 1), subject to the boundary value conditions: u'(0) - $\sum\limits^n_{i=1}{\alpha_i}u({\xi}_i)$ = 0, u'(1) + $\sum\limits^n_{i=1}{\alpha_i}u({\eta}_i)$ = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.679-686
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• 2010

This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.895-902
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• 2009

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

• Proceedings of the Korea Contents Association Conference
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• 2006.11a
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• pp.853-855
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• 2006

Today, the Publishing world goes to meet 'U-Publishing' which means the time of 'Ubiquitous Publishing 'in the Latin language. The concept of book evolves into the concept of U-Book beyond the concept of e-book from the concept of paper media book of the past Although the concept of book changes according to the times and media, there are design values which is changing and which isn't changing. We can regard these points of views as the immediate and the ultimate value. The immediate value means the values of the present time which explains the sprit of the time, and the ultimate value means what will not change beyond the time in spite of the difference of media which delivers design. This paper deals with the design of U-book concept which has been appear since 2n5 from the standpoint of the immediate and the ultimate value.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.