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Lianzhong Yang

Publications and source records attributed to Lianzhong Yang.

4 recordsLinked to original sources
arXiv2022

On value distribution of certain delay-differential polynomials

Given an entire function $f$ of finite order $ρ$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{λ+\varepsilon})+S(r,f)$, $λ<ρ$. Provided $α$, $β$ be similar small functions, we consider the zero distribution of $L(z,f)-αf^{n}-β$ for $n\geq 3$ and $n=2$, respectively. Our results are improvements and complements of Chen(Abstract Appl. Anal., 2011, 2011: ID239853, 1--9), and Laine (J. Math. Anal. Appl. 2019, 469(2): 808--826.), etc.

math.CV↗
arXiv2021

Some results on transcendental entire solutions of certain nonlinear differential-difference equations

In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $f^{2}(z)+\widetildeω f(z)f'(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}$, and $f^{n}(z)+ωf^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=p_{1}e^{λ_{1} z}+p_{2}e^{λ_{2} z}, \quad n\geq 3,$ where $ω$ is a constant, $\widetildeω, c, λ_{1}, λ_{2}, p_{1}, p_{2}$ are non-zero constants, $q, Q, u, v$ are polynomials such that $Q,v$ are not constants and $q,u\not\equiv0$. Our results are improvements and complements of some previous results.

math.CV↗
arXiv2020

Three results on transcendental meromorphic solutions of certain nonlinear differential equations

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: $f^{n}+P(f)=R(z)e^{α(z)}$ and $f^{n}+P_{*}(f)=p_{1}(z)e^{α_{1}(z)}+p_{2}(z)e^{α_{2}(z)}$ in the complex plane, where $P(f)$ and $P_{*}(f)$ are differential polynomials in $f$ of degree $n-1$ with coefficients being small functions and rational functions respectively, $R$ is a non-vanishing small function of $f$, $α$ is a nonconstant entire function, $p_{1}, p_{2}$ are non-vanishing rational functions, and $α_{1}, α_{2}$ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when $p_{1}, p_{2}$ are nonzero constants, and $°α_{1}=°α_{2}=1$. Our results are improvements and complements of Liao (Complex Var. Elliptic Equ. 2015, 60(6): 748--756), and Rong-Xu (Mathematics 2019, 7, 539), etc., which partially answer a question proposed by Li (J. Math. Anal. Appl. 2011, 375: 310--319).

math.CV↗