• 대한수학회보
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• 제51권5호
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• pp.1453-1467
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• 2014

In this paper, we consider the growth and existence of solutions of differential-difference equations of certain types. We also consider the differential-difference analogues of Br$\ddot{u}$ck conjecture and give a short proof on a theorem given by Li, Yang and Yi [18]. Our additional purpose is to explore the similarity or difference on some problems in differential, difference and differential-difference fields.

• 대한수학회보
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• 제50권5호
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• pp.1471-1479
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• 2013

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.

• 대한전기학회논문지:전력기술부문A
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• 제52권12호
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• pp.691-697
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• 2003

This paper proposes a current differential relay for transformer protection that operates in accordance with a blocking method based on the difference-function of a differential current. For magnetic inrush and over-excitation, discontinuities in the first-difference function of the differential current arise at the points of inflection, which correspond to the start and end of each saturation period of the core. These discontinuities are converted into the pulses in the second- and third-difference functions of the differential current. The magnitudes of the pulses are large enough to detect saturation of the core. A blocking signal is issued if the magnitude of the third-difference function exceeds the threshold and is maintained for three quarters of a cycle. The performance of the relay is assessed under various conditions with magnetic inrush, internal faults and external faults. The proposed blocking method can improve significantly the operating time of a relay and achieve high sensitivity of a relay.

• 대한수학회논문집
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• 제30권4호
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• 대한수학회지
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• 제35권4호
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• pp.881-890
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• 1998

Sufficient conditions for forced oscillations of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.

• 대한수학회논문집
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• 제39권1호
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• pp.117-125
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• 2024

In this paper, our focus is on exploring value sharing problems related to a transcendental entire function f and its associated differential-difference polynomials. We aim to establish some results which are related to differential-difference counterpart of the Brück conjecture.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1035-1044
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• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• 대한수학회보
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• 제60권3호
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• pp.593-610
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• 2023

In view of Nevanlinna theory, we investigate the meromorphic solutions of q-difference differential equations and our results give the estimates about counting function and proximity function of meromorphic solutions to these equations. In addition, some interesting results are obtained for two general equations and a class of system of q-difference differential equations.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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• pp.281-289
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• 2023

We investigate the value distribution of difference-differential polynomials of entire and meromorphic functions, which can be gazed as the Hayman's Conjecture. And also we study the uniqueness and existence for sharing common value of difference-differential polynomials.