• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.353-361
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• 2018

We develop a mathematical model of heat emission on the epidermis of a human body. We present a global existence theorem of solutions for a nonlinear model system of coupled partial differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.401-409
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• 2010

We study the existence of periodic solutions of Volterra equations by using the limiting equations and contraction mappings.

• East Asian mathematical journal
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• v.40 no.1
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• pp.85-94
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• 2024

In this paper we study the existence and multiplicity of positive solutions for p-Laplacian problems with a singular weight. Proofs mainly make use of Global Continuation Theorem and Fixed Point Index argument.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.229-234
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• 2005

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $x_{n+l} =\alpha+\frac{x_{n-1}^{p}}{x_{n}^{p}},\;\; n = 0, 1, ...$ is investigated, where all the coefficients are nonnegative real numbers.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.797-804
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• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.993-1000
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• 2006

Operating experience of steam generators has shown that cracks of various morphology frequently occur in the steam generator tubes. These cracked tubes can stay in service if it is proved that the tubes have sufficient safety margin to preclude the risk of burst and leak. Therefore, integrity assessment using exact limit load solutions is very important for safe operation of the steam generators. This paper provides global and local limit load solutions for surface cracks in the steam generator tubes. Such solutions are developed based on three-dimensional (3-D) finite element analyses assuming elastic-perfectly plastic material behavior. For the crack location, both axial and circumferential surface cracks, and for each case, both external and internal cracks are considered. The resulting global and local limit load solutions are given in polynomial forms, and thus can be simply used in practical integrity assessment of the steam generator tubes.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.507-516
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• 2016

In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation $$x_{n+1}={\frac{ax_{n-3}}{b-cx_{n-1}x_{n-3}}}$$, $n=0,1,{\ldots}$ where a, b, c are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.