• 대한수학회논문집
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• 제32권4호
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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.

• 대한수학회보
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• 제27권2호
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• pp.157-164
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• 1990

The purpose of this paper is to consider the inhomogeneous initial value problem (Fig.) in a Banach space X, where Z is the generator of an exponentially bounded C-semigroup in X, f9t) : [0, T].rarw.X and x.mem.X. Davies-Pang [1] showed the corresponding homogeneous equation, this is, the equation with f(t).iden.0, has a unique solution depending continuoously on the initial value x.mem.CD(z) in the $C^{-1}$-graph norm on CD(Z) when T=.inf..

• 대한수학회지
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• 제57권1호
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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.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.757-762
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• 2009

In allelic model $X\;=\;(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;{\int}^t_0\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. We can also obtain a new diffusion operator $L^*$ for diffusion coefficient and we prove that unique solution for $L^*$-martingale problem exists. In this note, we define new symmetric preserving transformation. Uniqueness for martingale problem and symmetric property will be proved.

• 한국경영과학회지
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• 제19권1호
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• pp.145-152
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• 1994

This paper deals with an economic design of acelerated life test under constant stresses where failure times are exponentially distributed. In this case the optimization criterion is the information amount per unit cost. Fisher's information matrix of exponential distribution's parameters and expected cost considering fixed and variable costs are obtained. The decision variable is the censoring time in the model. In the 2-level constant stress case, it is proved that the optimal solution exists and is unique under some condition. Numerical examples are also included.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• Bulletin of the Korean Chemical Society
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• 제31권11호
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• pp.3115-3117
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• 2010

The voltammetric study on a water-soluble calix[4]arene-diquinone-diacid (CDA) in pH 7.4 in the presence of $Ca^{2+}$ ion provided important information about the unique electrochemical behavior of CDA-$Ca^{2+}$ complex. Using CDA, $Ca^{2+}$ ion in aqueous solution was recognized quantitatively by voltammetric techniques.

• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

• East Asian mathematical journal
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• 제24권3호
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• pp.289-293
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• 2008

We recently showed in [5] a semilocal convergence theorem that guarantees convergence of Newton's method to a locally unique solution of a nonlinear equation under hypotheses weaker than those of the Newton-Kantorovich theorem [7]. Here, we first weaken Miranda's theorem [1], [9], [10], which is a generalization of the intermediate value theorem. Then, we show that operators satisfying the weakened Newton-Kantorovich conditions satisfy those of the weakened Miranda’s theorem.

• 호남수학학술지
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• 제24권1호
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• pp.35-41
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• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.