• 충청수학회지
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• 제33권2호
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• pp.205-217
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• 2020

We will introduce a new type of quartic functional equation and then investigate the stability for a quartic functional equation in a convex modular space.

• East Asian mathematical journal
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• 제35권3호
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.

• East Asian mathematical journal
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• 제39권3호
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• pp.319-329
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• 2023

In this paper, we consider a stochastic higher-order Kirchhoff-type equation with nonlinear damping and source terms. We prove the blow-up of solution for a stochastic higher-order Kirchhoff-type equation with positive probability or explosive in energy sense.

• 호남수학학술지
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• 제46권1호
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• pp.146-167
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• 2024

In this paper, we investigate the stability of the general decic functional equation $$\sum_{i=0}^{11}_{11}C_i(-1)^{11-i}f(x+iy)=0$$ in the sense of Rassias.

• 대한수학회논문집
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• 제39권3호
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• pp.731-737
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• 2024

In this paper, we study the Hyers-Ulam stability of the classical iterative functional equation fⁿ(x) = x, the Babbage equation, using strictly monotonic approximate solutions on a real interval.

• East Asian mathematical journal
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• 제40권5호
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• pp.515-526
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• 2024

We consider the initial value problem of the Schrödinger equation for an Euler operator 𝓡 on ℂⁿ that is an analogue of the harmonic oscillator in ℝⁿ. We get some regularity results of the Schrödinger equation on Fock spaces.

• 대한수학회논문집
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• 제23권3호
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• 대한수학회논문집
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• 제26권2호
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• pp.207-214
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• 2011

The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권4호
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• pp.505-514
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• 2008

방정식의 가해성 탐구는 수학사의 중요한 연구주제의 하나였으며, 삼차방정식과 사차방정식의 일반적인 해법은 교사양성기관의 현대대수학 교과에서 다루는 중요한 내용이다. 본 연구에서는 norm형식의 개념을 바탕으로 이차방정식의 근의 공식에 대한 방법유추를 통해 삼차방정식의 근의 공식을 유도하고, 삼차방정식의 근의 공식에 대한 방법유추를 통해 사차방정식의 근의 공식을 유도하였다.