• Honam Mathematical Journal
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• v.25 no.1
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• pp.83-91
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• 2003

We prove a unique continuation theorem for $C^{\infty}$ functions in pseudoconvex domains in ${\mathbb{C}}^{n}$. More specifically, we show that if ${\Omega}$ is a pseudoconvex domain in ${\mathbb{C}}^n$, if f is in $C^{\infty}({\Omega})$ such that for all multi-indexes ${\alpha},{\beta}$ with ${\mid}{\beta}{\mid}{\geq}1$ and for any positive integer k, there exists a positive constant $C_{{\alpha},{\beta},{\kappa}}$ such that $$|{\frac{{\partial}^{{\mid}{\alpha}{\mid}+{\mid}{\beta}{\mid}}f}{{\partial}z^{\alpha}{\partial}{\bar{z}}^{\beta}}{\mid}{\leq}C_{{\alpha},{\beta},{\kappa}}{\mid}f{\mid}^{\kapp}}\;in\;{\Omega}$$, and if there exists $z_0{\in}{\Omega}$ such that f vanishes to infinite order at $z_0$, then f is identically zero. We also have a sharp result for the case of strongly pseudoconvex domains.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.349-356
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• 2005

In this paper, by using the Leray-Schauder continuation theorem and Wirtinger-type inequalities, we establish the existence and uniqueness theorems for two-point boundary value problems of a certain class of fourth-order nonlinear differential equations.

• 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.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.695-703
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• 2002

The fractional order evolutionary integral equations have been considered by first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.369-380
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• 1999

As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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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.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.381-390
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• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.531-538
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• 1994

This paper is a continuation of [1] and [3]. In [3], the notion of BCI-G parts of BCI-algebras was introduced and various properties were investigated. In this paper, we consider the inverse of [3; Theorem 15], and define a KG-union BCI-algebra and investigate their properties.