• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.153-164
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• 2012

In this paper, we study the existence, non-existence, and multiplicity of positive solutions for a coupled telegraph system using the xed-point theorem of cone expansion/compression type, the upper-lowe solutions method, and xed point index theory.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.703-719
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• 2014

This paper is concerned with the traveling wave solutions of nonlocal dispersal models with nonlocal delays. The existence of traveling wave solutions is investigated by the upper and lower solutions, and the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate these results, a delayed competition model is considered by presenting the existence and nonexistence of traveling wave solutions, which completes and improves some known results. In particular, our conclusions can deal with the traveling wave solutions of evolutionary systems which admit large time delays reflecting intraspecific competition in population dynamics and leading to the failure of comparison principle in literature.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.553-558
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• 2008

The method of upper and lower solutions coupled with monotone iterative technique is used to obtain the results of existence and uniqueness for an anti-periodic boundary value problem of impulsive differential equations with delay.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1361-1370
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• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.735-747
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• 2018

This paper deals with the asymptotic behavior of solutions to the generalized MHD and Hall-MHD systems. Firstly, the upper bound for the generalized MHD and Hall-MHD systems is investigated in $L^2$ space. Then, the effect of the Hall term is analyzed. Finally, we optimize the upper bound of decay and obtain their algebraic lower bound for the generalized MHD system by using Fourier splitting method.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.1
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• pp.77-91
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• 2007

In this paper, we present a symbiotic evolutionary algorithm for multi-objective optimization. The goal in multi-objective evolutionary algorithms (MOEAs) is to find a set of well-distributed solutions close to the true Pareto optimal solutions. Most of the existing MOEAs operate one population that consists of individuals representing the entire solution to the problem. The proposed algorithm has a two-leveled structure. The structure is intended to improve the capability of searching diverse and food solutions. At the lower level there exist several populations, each of which represents a partial solution to the entire problem, and at the upper level there is one population whose individuals represent the entire solutions to the problem. The parallel search with partial solutions at the lower level and the Integrated search with entire solutions at the upper level are carried out simultaneously. The performance of the proposed algorithm is compared with those of the existing algorithms in terms of convergence and diversity. The optimization problems with continuous variables and discrete variables are used as test-bed problems. The experimental results confirm the effectiveness of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.209-220
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• 2007

In this paper, the existence and multiplicity of solutions of three-point p-Laplacian boundary value problems at resonance with one-sided Nagumo condition are studied by using degree theory and upper and lower solutions method. Some known results are improved.