• 대한수학회논문집
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• 제34권1호
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• pp.155-167
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• 2019

In this article we are concerned with some non-local problems of Kirchhoff type with Dirichlet boundary condition in Orlicz-Sobolev spaces. A result of the existence of infinitely many solutions is established using variational methods and Ricceri's critical points principle modified by Bonanno.

• 대한수학회지
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• 제56권5호
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.35-45
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• 2024

In this paper, we study the existence and multiplicity of nontrivial solutions for a p-Kirchhoff equation involving critical Sobolev-Hardy exponent by using variational methods and we need to estimate the energy levels.

• 대한수학회논문집
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• 제36권2호
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• 대한수학회논문집
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• 제36권1호
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• 대한기계학회논문집
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• 제15권1호
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• pp.145-153
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• 1991

본 연구에서는 Toh가 개발하여 stretchforming에 응용한 강소성 대변형 이론 을 압연문제에 적용하여 강소성 대변형 유한요소 프로그램을 개발하는데 있다.

• 한국전산구조공학회논문집
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• 제29권3호
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• pp.285-292
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• 2016

본 연구에서는 부유구조물 모델링의 효율성 및 응답의 정확성을 분석하기 위해 유체 영역을 압력으로 정의한 유탄성 해석법에 1차원 보-2차원 유체 결합의 1차원 문제와 2차원 판-3차원 유체 결합의 2차원 문제를 적용하여 수치해석을 수행하였다. 그리고 1차원 문제와 2차원 문제의 모델링 차원에 따른 응답을 비교하기 위해 다양한 평판의 변장비와 입사파의 조건을 적용하였다. 이에 따르면 강체거동의 영향이 큰 장주기파에서는 변장비가 변하더라도 두 문제의 유탄성 응답이 거의 유사하게 나타나지만 탄성거동의 영향이 지배적인 단주기파에서는 모델링 차원에 따라 뚜렷한 차이가 발생한다. 즉, 1차원 보 모델은 비록 입사파의 각도는 고려할 수 없지만 평판의 변장비가 클 경우에 유탄성 해석에 적용이 가능하다. 또한, 2차원 평판보다 단순화된 모델링 조건으로서 부유구조물의 전반적인 응답을 분석할 수 있을 뿐만 아니라 수치해석의 효율을 높일 수 있다.