• Title/Summary/Keyword: integral boundary condition

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POSITIVE SOLUTIONS FOR THE SECOND ORDER DIFFERENTIAL SYSTEM WITH STRONGLY COUPLED INTEGRAL BOUNDARY CONDITION

  • You-Young Cho;Jinhee Jin;Eun Kyoung Lee
    • East Asian mathematical journal
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    • v.40 no.1
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    • pp.37-50
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    • 2024
  • We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

SPECTRAL ANALYSIS FOR THE CLASS OF INTEGRAL OPERATORS ARISING FROM WELL-POSED BOUNDARY VALUE PROBLEMS OF FINITE BEAM DEFLECTION ON ELASTIC FOUNDATION: CHARACTERISTIC EQUATION

  • Choi, Sung Woo
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.71-111
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    • 2021
  • We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

Properties of integral operators in complex variable boundary integral equation in plane elasticity

  • Chen, Y.Z.;Wang, Z.X.
    • Structural Engineering and Mechanics
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    • v.45 no.4
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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.

EXISTENCE OF POSITIVE SOLUTIONS FOR THE SECOND ORDER DIFFERENTIAL SYSTEMS WITH STRONGLY COUPLED INTEGRAL BOUNDARY CONDITIONS

  • Lee, Eun Kyoung
    • East Asian mathematical journal
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    • v.34 no.5
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    • pp.651-660
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    • 2018
  • This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS

  • Soenjaya, Agus L.
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.497-502
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    • 2022
  • Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

FINITE DIFFERENCE SCHEME FOR SINGULARLY PERTURBED SYSTEM OF DELAY DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • SEKAR, E.;TAMILSELVAN, A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.3
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    • pp.201-215
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    • 2018
  • In this paper we consider a class of singularly perturbed system of delay differential equations of convection diffusion type with integral boundary conditions. A finite difference scheme on an appropriate piecewise Shishkin type mesh is suggested to solve the problem. We prove that the method is of almost first order convergent. An error estimate is derived in the discrete maximum norm. Numerical experiments support our theoretical results.

NUMERICAL METHOD FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION DIFFUSION EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

  • Raja, Velusamy;Tamilselvan, Ayyadurai
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.1015-1027
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    • 2019
  • A class of systems of singularly perturbed convection diffusion type equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The suggested method is of almost first order convergence. An error estimate is derived in the discrete maximum norm. Numerical examples are presented to validate the theoretical estimates.