• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.851-863
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• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

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

• 대한수학회논문집
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• 제22권1호
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• pp.53-64
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• 2007

In this paper, we apply the generalized quasilinearization technique to a forced Duffing equation with three-point mixed nonlinear nonlocal boundary conditions and obtain sequences of upper and lower solutions converging monotonically and quadratically to the unique solution of the problem.

• 대한수학회지
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• 제40권4호
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• pp.681-693
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• 2003

In this paper, we first prove that there are no automorphism orbits accumulating at a boundary point of the largest isolated finite type. We also present a generalization of the results of Isaev and Krantz on the structure of the orbit accumulation points.

• 대한수학회보
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• 제48권4호
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• pp.705-712
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• 2011

In this paper, we investigate the boundary control of semilinear neutral evolution systems with a nonlocal condition by using the Banach fixed point theorem.

• Proceedings of the Jangjeon Mathematical Society
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• 제20권2호
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• 문화기술의 융합
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• 제4권4호
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• pp.367-372
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• 2018

본 논문은 무선 센서 네트워크의 경계노드를 효과적으로 검출하는 알고리즘을 제안한다. 경계노드는 센서 네트워크의 외부 경계 또는 홀의 경계에 존재하는 센서이다. 제안한 알고리즘은 센서의 위치정보만을 이용하여 네트워크의 경계노드를 검출한다. 또한 검출 속도를 향상시키기 위해 센서는 거리에 따라 근접한 센서와의 중첩영역을 먼저 계산한다. 알고리즘의 동작을 검증하기 위해 시뮬레이션을 수행하였다. 시뮬레이션에서 현실 세계를 최대한 반영하기 위해 정해진 영역에 여러 개의 장애물을 설치하고 센서의 개수를 500~1500개 범위에서 다르게 배치하였다. 시뮬레이션을 통하여 제안한 알고리즘이 네트워크 외부 및 홀의 경계에 존재하는 경계노드들을 효과적으로 검출하는 것을 확인하였다.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.457-470
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• 2008

This paper is concerned with the robust boundary control of the chemotaxis reaction diffusion system. That is, we show that the existence of the saddle point for the robust control problem when the control and the disturbance are given by the boundary condition.