• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.59-74
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• 2010

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

• 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.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 applied mathematics & informatics
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• v.27 no.1_2
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• 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.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1253-1268
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• 2006

We develop the upper and lower solutions method for the four point problem relative to second order differential equations in order to obtain the existence of solution.

• Computers and Concrete
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• v.23 no.3
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• pp.171-188
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• 2019

This study proposed a new and efficient 2D damage-plasticity model within the framework of Isogeometric analysis (IGA) for the geometrically nonlinear damage analysis of concrete. Since concrete exhibits complicated material properties, two internal variables are introduced to measure the hardening/softening behavior of concrete in tension and compression, and an implicit gradient-enhanced formulation is adopted to restore the well-posedness of the boundary value problem. The numerical results calculated by the model is compared with the experimental data of three benchmark problems of plain concrete (three-point and four-point bending single-notched beams and four-point bending double-notched beam) to illustrate the geometrical flexibility, accuracy, and robustness of the proposed approach. In addition, the influence of the characteristic length on the numerical results of each problem is investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.1
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• pp.31-38
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• 2008

This paper deals with the nonlinear optimal control approach to helicopter maneuver problems using the indirect method. We apply a penalty function to the integral deviation from a prescribed trajectory to convert the system optimality to an unconstrained optimal control problem. The resultant two-point boundary value problem has been solved by using a multiple-shooting method. This paper focuses on the model selection strategies to resolve the problem of numerical instability and high wait time when a high fidelity model with rotor dynamics is applied. Four different types of helicopter models are identified, two of which are linear models with or without rotor models, as well as two models which include the nonlinear mathematical model for rotor in its formulation. The relative computation time and the number of function calls for each model are compared in order to provide a guideline for the selection of helicopter model.

• Economic and Environmental Geology
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• v.29 no.3
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• pp.335-343
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• 1996

The dipole-dipol electrical resistivity survey was conducted to investigate the probable contamination of the Han river by leachate from the near-by Nanjido Landfill. The survey line of 3 km was set along the unpaved road toward the Han river. For the convenience of the field work, the survey line was divided into four segments. The complete two-dimensional resistivity section was constructed by connecting the inversion result of each segment. Gravity survey was also carried out along the profile parallel to the resistivity line. Near surface resistivity generally appeared to be of very low value in most part of the survey area and the boundary between the alluvium layer and underlying basement rocks is well discriminated on the resistivity section. These results agree well with those of the preceding Schlumberger depth sounding made at adjacent area by Lee and fun (1995). The variation of thickness of the alluvium layer delineated by gravity anomaly profile also correlates well with the result of the resistivity survey on the qualitative basis. The problem of contamination by leachate from the Nanjido Landfill, where various waste materials have been dumped without any proper treatment facilities, has been remains unsolved yet. Therefore, we present the most probable passages of leachate flow based on the survey results and have briefly discussed about measure for contamination control. Considering the thickness of alluvium and the possible existence of fractured zone, the middle point between 1st and 2nd landfill and the midst of 1st landfill are the most hazardous regions to make leachates flow into the Han river. Since large amounts of leachates are observed from the test wells located on the lines extending from the border between the 1st and 2nd landfill and the middle of the lst landfill, contamination protection barriers are strongly recommended near these regions.