• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.173-186
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• 2015

In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.201-211
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• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.45-51
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• 2017

In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy non-linear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.

• Bulletin of the Korean Chemical Society
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• v.18 no.12
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• pp.1260-1264
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• 1997

The phase-transfer reagent (PTC), ethyl tri-n-octylammonium bromide (ETABr), strongly catalyzes the reaction of p-nitrophenyldiphenylphosphinate (p-NPDPIN) with benzimidazole (BI) and its anion (BI-). In ETABr solutions, the dephosphorylation reactions exhibit higer than first order kinetics with respect to the nucleophile, BI, and ETABr, suggesting that reactions are occuring in small aggregates of the three species including the substrate, whereas the reaction of p-NPDPIN with OH- is not catalyzed by ETABr. This behavior for the drastic rate-enhancement of the dephosphorylation is refered as 'aggregation complex model' for reactions of hydrophobic organic phosphinates with benzimidazole in hydrophobic quarternary ammonium salt solutions.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.729-744
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• 2021

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodynamic model based on the coupled Navier-Stokes-Poisson-Nernst-Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the L^p interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

• East Asian mathematical journal
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• v.38 no.1
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• pp.13-20
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• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.495-511
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• 2017

In this paper, we consider the system of three elliptic equations using two critical point theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.8
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• pp.1137-1144
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• 1989

In this paper, for eliminating the spurious solutions which have been necessarily included in the solutions of earlier vectorial finite-element method, we have proposed the improved finite-element method for the analysis of dielectric waveguides in the three-component magnetic field.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.