• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.59-74
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• 2010

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.487-494
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• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.306-310
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• 2004

In this paper, we consider the Ring Loading Problem with integer demand splitting (RLP). The problem is given with a ring network, in which a required traffic requirement between each selected node pair must be routed on it. Each traffic requirement can be routed in both directions on the ring network while splitting each traffic requirement in two directions only by integer is allowed. The problem is to find an optimal routing of each traffic requirement which minimizes the capacity requirement. Here, the capacity requirement is defined as the maximum of traffic loads imposed on each link on the network. We formulate the problem as an integer program. By characterizing every extreme point solution to the LP relaxation of the formulation, we show that the optimal objective value of the LP relaxation is equal to p or p+0.5, where p is a nonnegative integer. We also show that the difference between the optimal objective value of RLP and that of the LP relaxation is at most 1. Therefore, we can verify that the optimal objective value of RLP is p+1 if that of the LP relaxation is p+0.5. On the other hand, we present a strengthened LP with size polynomially bounded by the input size, which provides enough information to determine if the optimal objective value of RLP is p or p+1.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1109-1118
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• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1241-1250
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• 2012

We prove the maximum principle and the comparison principle of $p$-harmonic functions via $p$-harmonic boundary of graphs. By applying the comparison principle, we also prove the solvability of the boundary value problem of $p$-harmonic functions via $p$-harmonic boundary of graphs.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• Journal of the Korea Society of Computer and Information
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• v.20 no.11
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• pp.105-110
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• 2015

This paper deals with a newly proposed algorithm for stable marriage problem, which I coin threshold algorithm. The proposed algorithm firstly constructs an $n{\times}n$ matrix of the sum of each sex's preference over the members of the opposite sex. It then selects the minimum value from each row and column to designate the maximum value of the selected as the sum threshold $p^*_{ij}$. It subsequently deletes the maximum preference $_{mzx}p_{ij}$ from a matrix derived from deleting $p_{ij}$ > $p^*_{ij}$, until ${\mid}c_i{\mid}=1$ or ${\mid}c_j{\mid}=1$. Finally, it undergoes an optimization process in which the sum preference is minimized. When tested on 7 stable marriage problems, the proposed algorithm has proved to improve on the existing solutions.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.