• Journal of Korean Society for Atmospheric Environment
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• 제15권E호
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• pp.65-71
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• 1999

The log-normal size distribution theories developed recently for aerosol coagulation are reviewed. The analytical solutiosn to Brownian coagulation developed recently for various particle size regimes are reviewed. In order to describe the evolution of the size distribution of a coagulating aerosol over the entire size range, the analytical solutions developed individually for the free-molecule regime, the transition regime, the nearcontinuum regime, and the continuum regime have been combined. The work described here represents the first analytical solution to the aerosol coagulation problem covering the entire particle size range.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

• 대한수학회논문집
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• 제37권3호
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• pp.893-904
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• 2022

In this note, we apply a maximum principle related to volume growth of a complete noncompact Riemannian manifold, which was recently obtained by Alías, Caminha and do Nascimento in [4], to establish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.

• 대한수학회보
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• 제48권6호
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.295-309
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• 2020

In this paper we study the growth of solutions of some non-linear complex differential equations in connection to Brück conjecture using the theory of complex differential equation.

• 대한수학회보
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• 제49권5호
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• pp.911-921
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• 2012

In this paper, the radial oscillation of the solutions of higher order homogeneous linear differential equation $$f^{(k)}+A_{n-2}(z)f^{(k-2)}+{\cdots}+A_1(z)f^{\prime}+A_0(z)f=0$$ with transcendental entire function coefficients is studied. Results are obtained to extend some results in [Z. Wu and D. Sun, Angular distribution of solutions of higher order linear differential equations, J. Korean Math. Soc. 44 (2007), no. 6, 1329-1338].

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1011-1016
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• 2011

In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equation on $R^N$. we obtained the results under different suitable conditions on the locally H$\"{o}$lder continuous nonlinearity f(x, u), we needn't any mono-tonicity condition about the nonlinearity.

• 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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• 제34권1호
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• pp.135-146
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• 1997

For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.65-73
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• 2021

In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation L(f) = b (z) f + c (z), where L(f) is a linear differential polynomial and b (z), c (z) are entire functions and give some of its applications on sharing value problems.