• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제16권4호
• /
• pp.327-344
• /
• 2009

In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale $\mathbb{T}$ $$\{{{{{{x^{\bigtriangleup\bigtriangleup}(t)+f(t,\;y(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}\atop{y^{\bigtriangleup\bigtriangleup}(t)+g(t,\;x(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}}\atop{\alpha_1x(a)-\beta_1x^{\bigtriangleup}(a)=\gamma_1x(\sigma(b))+\delta_1x^{\bigtriangleup}(\sigma(b))=0,}}\atop{\alpha_2y(a)-\beta_2y^{\bigtriangleup}(a)=\gamma_2y(\sigma(b))+\delta_2y^{\bigtriangleup}(\sigma(b))=0,}}$$ where $\alpha_i$, $\beta_i$, $\gamma_i\;{\geq}\;0$ and $\rho_i=\alpha_i\gamma_i(\sigma(b)-a)+\alpha_i\delta_i+\gamma_i\beta_i$ > 0(i = 1, 2), f(t, y) may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems $x^{\bigtriangledown\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangledown}(t)$ + g(t, x(t)) = 0, $x^{\bigtriangleup\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangleup\bigtriangledown}(t)$ + g(t, x(t)) = 0, and $x^{\bigtriangledown\bigtriangleup}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangleup}(t)$ + g(t, x(t)) = 0 satisfying similar boundary conditions.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1309-1331
• /
• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• 대한수학회지
• /
• 제47권5호
• /
• pp.985-1000
• /
• 2010

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.

• Nonlinear Functional Analysis and Applications
• /
• 제29권2호
• /
• pp.545-558
• /
• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.501-515
• /
• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• 한국측량학회:학술대회논문집
• /
• 한국측량학회 2010년 춘계학술발표회 논문집
• /
• pp.11-13
• /
• 2010

Combined with the indeterminate boundaries of spatial objects, n:m correspondences makes an object-based matching be a complex problem. In this study, we model the boundary of a polygon object with fuzzy model and describe their overlapping relations as a weighted bipartite graph. Then corresponding pairs including 1:0, 1:1, 1:n and n:m relations are identified using a spectral singular value decomposition.

• 대한기계학회논문집A
• /
• 제30권8호
• /
• pp.949-956
• /
• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• 한국생산제조학회지
• /
• 제20권2호
• /
• pp.139-144
• /
• 2011

This paper presents a boundary element application to determine the optimal impressed current densities at defect position on the pipe line. In this protection paint, enough current must be impressed to lower the potential distribution on the metal surface to the critical values. The optimal impressed current densities are determined in order to minimize the power supply for protection. This inverse problem was formulated by employing the boundary element method. Since the system of linear equations obtained was ill-conditioned, including singular value decomposition, conjugate gradient method were applied and the accuracies of these estimation. Several numerical examples are presented to demonstrate the practical applicability of the proposed method.

• 대한기계학회논문집A
• /
• 제20권4호
• /
• pp.1275-1289
• /
• 1996

The plane elasticity problem of collinear cracks in a layered medium is investigated. The medium is modeled as bonded structure constituted from a surface layer and a semi-infinite substrate. Along the bond line between the two dissimilar homegeneous constituents, it is assumed that as interfacial zone having the functionally graded, nonhomogeneous elastic modulus exists. The layered medium contains three collinear cracks, one in each constituent material oriented perpendicular to the nominal interfaces. The stiffness matrix formulation is utilized and a set of homogeneous conditions relevant to the given problem is readily satisfied. The proposed mixed boundary value problem is then represented in the form of a system of integral equations with Cauchy-type singular kernels. The stress intensity factors are defined from the crack-tip stress fields possessing the standard square-root singular behavior. The resulting values of stress intensity factors mainly address the interactions among the cracks for various crack sizes and material combinations.

• 한국정밀공학회지
• /
• 제19권5호
• /
• pp.81-88
• /
• 2002

An interface crack of a piezoelectric medium bonded between an elastic layer and a half-space is analyzed using the theory of linear piezoelectricity. Both out-of-plane mechanical and in-plane electrical loads are applied to the piezoelectric laminate. By the use of courier transforms, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically to determine the stress intensity factors. Numerical analyses for various material combinations are performed and the results are discussed.