• Honam Mathematical Journal
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• v.30 no.2
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• pp.391-397
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• 2008

The existence of solutions and the occurrence of a Hopf bifurcation for the free boundary problems with Pushchino dynamics was shown in [1]. In this paper, we shall show a Hopf bifurcation occurs for the free boundary for Pushchino dynamics with a spatial dependency.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.561-570
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• 2021

In this paper, applying the bifurcation method and topological analysis, we investigate the global structures of solutions for one-dimensional Minkowski-curvature problems under certain behavior of nonlinear term near zero.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.14-24
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• 2018

Several typical hyper-elastic constitutive models that encompass both conventional and advanced ones were investigated for the application of instability problems, including the biaxial tension of a rubber patch and inflation of spherical or cylindrical balloons. The material models included the neo-Hookean model, Mooney-Rivlin model, Gent model, Arruda-Boyce model, Fung model, and Pucci-Saccomandi model. Analyses can be done using membrane equations with particular strain energy density functions. Among the typical strain energy density functions, Kearsley's bifurcation for the Treloar's patch occurs only with the Mooney-Rivlin model. The inflation equation is so generalized that a spherical balloon and tube balloons can be taken into account. From the analyses, the critical material parameters and limit points were identified for material models in terms of the non-dimensional pressure and inflation volume ratio. The bifurcation was then identified and found for each material model of a balloon. When the finite element method was used for the structural instability problems of rubber-like materials, some careful treatments required could be suggested. Overall, care must be taken not only with the analysis technique, but also in selecting constitutive models, particularly the instabilities.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.331-343
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• 2020

This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems -Δv = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ R^N : r₁ < |x| < r₂} with 0 < r₁ < r₂, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s₁(x)) = h(x, s₂(x)) = 0 for suitable positive, concave function s₁ and negative, convex function s₂, as well as sh(x, s) > 0 for s ∈ ℝ \ {0, s₁(x), s₂(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.

• Journal of Ocean Engineering and Technology
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• v.11 no.4
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.395-402
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• 1999

This paper discusses the theoretical researches subject to elastic buckling problems of the structures. The purpose is to ensure the characteristic of buckling be true by arc-length method and the finite element method. The difficulties in processes calculating the equilibrium curve after buckling is to get the equilibrium owe near singular point at which the determinant of stiffness matrix is zero. The purpose of the load-displacement curve is to determine the buckling load of the structure, and further to get the information about the characteristic after buckling. Here, this paper expresses the incremental solution at particular point by the linear combination of both homogeneous mode and particular mode, then uses the method which gets the unknown parameter including this function, through trial-and-error method including modified N-R convergence process. Finally, this paper describes the multiple bifurcation of truss dome as the numerical examples according to this algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.9-18
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• 1996

The primary objective of this paper is to grasp many characteristics of buckling behavior of latticed spherical domes under various conditions. The Arc-Length Method proposed by E.Riks is used for the computation and evaluation of geometrically nonlinear fundamental equilibrium paths and bifurcation points. And the direction of the path after the bifurcation point is decided by means of Hosono's concept. Three different nonlinear stiffness matrices of the Slope-Deflection Method are derived for the system with rigid nodes and results of the numerical analysis are examined in regard in geometrical parameters such as slenderness ratio, half-open angle, boundary conditions, and various loading types. But in case of analytical model 2 (rigid node), the post-buckling path could not be surveyed because of Newton-Raphson iteration process being diversed on the critical point since many eigenvalues become zero simultaneously.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• Korean Journal of Remote Sensing
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• v.10 no.1
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• pp.43-53
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• 1994

By Using MOS-1 satellite image(taken on 24 April 1990, after slash and burn), Shifting cultivation areas were estimated for the sub-basin area. In tropical region to analyse the correlation between shifting cultivation rate and bifurcation rate network which was calculated from topographic map, PC Arc - Info and IDRISI GIS software were used. As the distribution rate of shifting cultivation increases, the bifurcation rate is high. From the correlation analysis between the shifting cultivation and drainage network, it was found that shifting cultivation leads to land degradation and head erosion at the stream valley. To prevent such problems, it is mecessary that shifting cultivation areas should be converted to permanent paddy fields.