• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.245-253
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• 2007

In this paper, the existence of bounded positive solution of the second-order nonlinear neutral differential equations are studied. Some new sufficient conditions are given. Furthermore, examples given show that the results here are almost sharp.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• 대한수학회논문집
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• 제22권3호
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• pp.465-474
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• 2007

With the help of the coincidence degree and the related continuation theorem, we explore the existence of at least two periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system with control. Some easily verifiable sufficient criteria are established for the existence of at least two positive periodic solutions.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1435-1446
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• 2009

In this paper we investigate the blow up properties of the positive solutions to a semi linear parabolic system with coupled nonlocal sources $u_t={\Delta}u+k_1{\int}_{\Omega}u^{\alpha}(y,t)v^p(y,t)dy,\;v_t={\Delta}_v+k_2{\int}_{\Omega}u^q(y,t)v^{\beta}(y,t)dy$ with non local Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.

• Kyungpook Mathematical Journal
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• 제56권2호
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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.

• 한국염색가공학회지
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• 제13권6호
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• pp.435-440
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• 2001

This study investigates the rheological properties of in-situ polymerized solutions of polyacrylonitrile(PAN) and acrylonitrile(AN) -itaconic acid(IA) in dimethyl sulfoxide(DMSO) in terms of temperature, concentration, and time. The complex viscosity and storage modulus of the solutions were generally increased with elapsing time, which is ascribable to the three-dimensional pseudostructures formed by strong inter- or Intra-molecular attractions through Polar -CN and -COOH groups. The three-dimensional pseudonetworks would lead to relation of the acrylic solutions in long term. This was more noticeable at higher temperature within the temperature range examined. In the case of 20% solutions one can not observe lower Newtonian flow region in the viscosity curve. Disappearance of lower Newtonian flow region is indicative of heterogeneity of the solution system. Casson Plot of the viscosity data revealed that 20% solutions of PAN and AN-IA copolymer in DMSO clearly demonstrated positive yield stress, ascertaining formation of pseudostructures in the solution systems.

• 한국염색가공학회지
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• 제13권6호
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• pp.77-77
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• 2001

This study investigates the rheological properties of in-situ polymerized solutions of polyacrylonitrile(PAN) and acrylonitrile(AN)-itaconic acid(IA) in dimethyl sulfoxide(DMSO) in terms of temperature, concentration, and time. The complex viscosity and storage modulus of the solutions were generally increased with elapsing time, which is ascribable to the three-dimensional pseudostructures formed by strong inter- or intra-molecular attractions through Polar -CN and -COOH groups. The three-dimensional pseudonetworks would lead to gelation of the acrylic solutions in long term. This was more noticeable at higher temperature within the temperature range examined. In the case of 20% solutions one can not observe lower Newtonian flow region in the viscosity curve. Disappearance of lower Newtonian flow region is indicative of heterogeneity of the solution system. Casson Plot of the viscosity data revealed that 20% solutions of PAN and AN-IA copolymer in DMSO clearly demonstrated positive yield stress, ascertaining formation of pseudostructures in the solution systems.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.101-108
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• 2008

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\"{o}$dinger equation: $iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}$ = 0, where a is real constant, 1 $\leq$ d < n is a integer is a positive constant, and x = $(x_1,x_2,\cdots,x_n)\;\in\;R^n$. For some admissible ${\alpha}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.201-216
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• 2007

In this paper we consider the difference equation $$x_{n+1}=\frac{a+bx_{n-k}\;-\;cx_{n-m}}{1+g(x_{n-l})}$$ where a, b, c are nonegative real numbers, k, l, m are nonnegative integers and g(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation.