• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• 대한수학회논문집
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• 제38권3호
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• pp.925-935
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• 2023

In this paper, we consider a boundary value problem for a sixth order difference equation. We prove the monotone behavior of the eigenvalue of the problem as the coefficients in the difference equation change values and the existence of a positive solution for a class of problems.

• Structural Engineering and Mechanics
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• 제45권4호
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.17-28
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• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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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.

• 대한수학회지
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• 제54권1호
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• pp.249-265
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• 2017

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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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.

• Structural Engineering and Mechanics
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• 제4권2호
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• pp.191-202
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• 1996

This paper presents a construction of adaptive boundary element for the problem with mixed boundary conditions such as heat transfer between heated body surface and surrounding medium. The scheme is based on the sample point error analysis and on the extended error indicator, proposed earlier by the authors for the potential and elastostatic problems, and extended successfully to multidomain and thermoelastic analyses. Since the field variable is connected with its derivative on the boundary, their errors are also interconnected by the specified condition. The extended error indicator on each boundary element is modified to meet with the situation. Two numerical examples are shown to indicate the differences due to the prescribed boundary conditions.

• 대한수학회논문집
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• 제10권3호
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• pp.751-758
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• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.

• 대한수학회지
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• 제34권2호
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• pp.395-405
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• 1997

A globality of the Hopf bifurcation in a free boundary problem for a parabolic partial differential equation is investigated in this paper. We shall examine the global behavior of the Hopf critical eigenvalues and and apply the center-index theory to show the globality.