• East Asian mathematical journal
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• v.31 no.3
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• pp.321-335
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• 2015

The existence of at least one solution to a system of multipoint boundary value problems on an infinite interval is investigated by using the Alternative of Leray-Schauder.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Journal of Korean society of Dental Hygiene
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• v.9 no.4
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• pp.836-848
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• 2009

Objectives : This study was conducted to evaluated the subjective oral health state related periodontal disease of elderly people. Methods : Data were collected through the National Health and Nutrition Survey in 2005. Participants consisted of 1,091 elderly people above 65 years old. Independent variables in the survey were social characteristic, health behavior, oral health condition, oral health management. The data were analyzed by using the SPSS 12.0. Results : The more elderly people of 69.0% recognized own oral health as is not healthy, elderly people of 74.0% recognized own oral health as is not healthy about subjective oral health and a lot of stressed(82.8%) has felt highly about periodontal disease(p<0.001). Respondents of have a sound teeth(58.9%), have a lower denture(75.0%) and have a no problem in mastication(74.5%) has felt highly about periodontal disease(p<0.001). Elderly people recognized own oral health as is not healthy about subjective oral health were 0.316 times(p<0.01), elderly people recognized own oral health as is common healthy about subjective oral health were 0.241 times(p<0.001), a lot of stressed were 1.410 times has felt highly about periodontal disease. Elderly people of have a lower denture were 1.159 times, have a upper denture were 1.159 times, have a lower and upper denture were 0.464 times has felt highly about periodontal disease(p<0.05). Also respondents of have a no problem in mastication were 7.464 times compared with problem in mastication(p<0.001). Conclusions : Quality of life from disease of Korean elderly people can be fallen, and improve quality of life that medical treatment is healthy numerical value state numerical value state. Study's findings of above may be used to inform the importance of health numerical value state while establish dental health policy that is string.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1817-1826
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• 2013

The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [11].

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.1
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• pp.206-211
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• 2006

The quantification analysis problem is that how the m entities that have n characteristics can be linked to p-dimension space to reflect the similarity of each entity In this paper, the optimization approach for the quantification analysis problem using neural networks is suggested, and the performance is analyzed The computation of average variation volume by mean field theory that is analytical approximated mobility of a molecule system and the annealed mean field neural network approach are applied in this paper for solving the quantification analysis problem. As a result, the suggested approach by a mean field annealing neural network can obtain more optimal solution than the eigen value analysis approach in processing costs.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.349-361
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• 2022

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V₁. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.

• Journal of the military operations research society of Korea
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• v.31 no.1
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• pp.122-129
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• 2005

In discrete red and black, you can stake any amount s in your possession, but the value of s takes positive integer value. Suppose your goal is N and your current fortune is ${\Large\;f},\;with\;O<{\Large\;f}. You win back your stake and as much more with probability p and lose your stake with probability, q=1-p. In this study, we consider optimum strategies for this game with the value of p less than ${\frac{1}{2}}$ where the house has the advantage over the player. It is shown that the optimum strategy at any ${\Large\;f}$ is the DBold strategy which is to play boldly in discrete red and black when $p<{\frac{1}{2}}$. And then, we perform the simulation study to show that this strategy, which is to bet as much as you can, is optimal in discrete case.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.457-469
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• 2008

In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary value problem with p-Laplacian: $\{{{{(\phi_p(u'))'\;+\;f(t,u(t))=0, \;0<t<1,} \atop u'(0)={\sum}{^{m-2}_{i=1}}\;a_iu'(\xi_i),} \atop u(1)={\sum}{^k_{i=1}}\;b_iu(\xi_i)\;-\;{\sum}{^s_{i=k+1}}\;b_iu(\xi_i)\;-\;{\sum}{^{m-2}_{i=s+1}}\;b_iu'(xi_i),}$ where ${\phi}_p(s)$ is p-Laplacian operator, i.e., ${\phi}_p(s)=\mid s\mid^{p-2}s$, p>1, ${\phi}_q\;=\;({\phi}_p)^{-1}$, $\frac{1}{p}+\frac{1}{q}=1$, $1\;{\leq}\;k\;{\leq}\;s\;{\leq}m\;-\;2$, $b_i\;{\in}\;(0,+{\infty})$ with $0\;<\;{\sum}{^k_{k=1}}\;b_i\;-\;{\sum}{^s_{i=k+1}}\;b_i\;<\;1$, $0\;<\;{\sum}{^{m-2}_{i=1}}\la_i\;<\;1$, $0\;<\;{\xi}_1\;<\;{\xi}_2\;<\;{\cdots}\;<\;{\xi}_{m-2}\;<\;1$, $f\;{\in}\;C([0,\;1]\;{\times}\;[0,\;+{\infty}),\;[0,\;+{\infty}))$. We show that there exists one or two positive solutions by using fixed-point theorem for operator on a cone. The conclusions in this paper essentially extend and improve the known results.