• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1189-1200
• /
• 2009

The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.51-61
• /
• 2018

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+({\Delta}_cf)^2={\beta}^2$, $f^2+({\Delta}_cf)^2=R$, $f{^{\prime}^2}+({\Delta}_cf)^2=R$ and $f^2+(f(z+c))^2=R$, where ${\beta}$ is a nonzero small function of f and R is a nonzero rational function respectively. These discussions extend one related result due to C. C. Yang et al. in some sense

• Communications of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.361-373
• /
• 2017

In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of $Br{\ddot{u}}ck$ conjecture. In other words, we consider ${\Delta}_{\eta}f(z)=f(z+{\eta})-f(z)$ and f'(z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where ${\eta}{\in}{\mathbb{C}}{\backslash}\{0\}$ is a constant such that $f(z+{\eta})-f(z){\not\equiv}0$.

• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.439-448
• /
• 2007

In the paper, we use the theory of normal family to study the problem on entire function that share a finite non-zero value with their derivatives and prove a uniqueness theorem which improve the result of J.P. Wang and H.X. Yi.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.247-260
• /
• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.1061-1073
• /
• 2020

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Q_d(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p₁(z), p₂(z), p₃(z) are non-vanishing rational functions, and α₁(z), α₂(z), α₃(z) are nonconstant polynomials such that α'₁(z), α'₂(z), α'₃(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.205-226
• /
• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.865-870
• /
• 2018

We show that if two nonconstant meromorphic functions f and g on $\mathbb{C}$ sharing some finite sets IM, then there is a nonconstant rational function R(z) such that R(f) = R(g).

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.785-795
• /
• 2018

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.40-45
• /
• 1991

This paper deals with the design of feedback controllers which minimize the $H^{\infty}$-norm of the weighted sensitivity function. Using the Lagrange multiplier method and the Nevanlinna-Pick interpolation theory, an algorithm which stabilizes a plant and makes the output to track the reference signal is proposed..