Results 41 to 50 of about 6,503,100 (217)
AIMS Mathematics, 2022 By using Nevanlinna of the value distribution of meromorphic functions, we investigate the transcendental meromorphic solutions of the non-linear differential equation $ \begin{equation*} f^{n}+P_{d}(f) = p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}+p_{3}
Linkui Gao, Junyang Gao
doaj +1 more source
The growth of entire solutions of certain nonlinear differential-difference equations
AIMS Mathematics, 2022 This paper is concerned with entire solutions of nonlinear differential-difference equations. We will characterize the growth of entire solutions for two classes of nonlinear differential-difference equations.
Wenjie Hao, Qingcai Zhang
doaj +1 more source
AIMS Mathematics, 2022 This article is concerned with the existence of entire solutions for the following complex second order partial differential-difference equation $ \left(\frac{\partial^2 f(z_1, z_2)}{\partial z_1^2}+\frac{\partial^2 f(z_1, z_2)}{\partial z_2^2 ...
Wenju Tang, Keyu Zhang, Hongyan Xu
doaj +1 more source
On the equation fn + (f″)m ≡ 1
Demonstratio Mathematica, 2023 Let nn and mm be two positive integers, and the second-order Fermat-type functional equation fn+(f″)m≡1{f}^{n}+{({f}^{^{\prime\prime} })}^{m}\equiv 1 does not have a nonconstant meromorphic solution in the complex plane, except (n,m)∈{(1,1),(1,2),(1,3 ...
Dang Guoqiang
doaj +1 more source
Entire solutions of two certain types of quadratic trinomial q-difference differential equations
AIMS Mathematics, 2023 The main purpose of this paper is to find the explicit forms for entire solutions of two certain types of Fermat-type q-difference differential equations.
Zhenguang Gao, Lingyun Gao , Manli Liu
doaj +1 more source
On the differentiability of T(r,f)
International Journal of Mathematics and Mathematical Sciences, 1982 It is well known that T(r,f) is differentiable at least for r>r0. We show that, in fact, T(r,f) is differentiable for all but at most one value of r, and if T(r,f) fails to have a derivative for some value of r, then f is a constant times a quotient of ...
Douglas W. Townsed
doaj +1 more source
AIMS Mathematics, 2021 In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $ \begin{eqnarray*} f^{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e^{Q(z)}f(z+c) = u(z)e^{v(z)}, \end{eqnarray*} $ and $ \
Nan Li, Jiachuan Geng, Lianzhong Yang
doaj +1 more source
The Jacobi matrices approach to Nevanlinna-Pick problems [PDF]
, 2010 A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\bR_0$-functions gives rise to a linear pencil $H-\lambda J$, where $H$ and $J$ are Hermitian tridiagonal matrices.
Achiezer +51 more
core +2 more sources
Some Properties of Meromorphic Solutions of Systems of Complex q-Shift Difference Equations
Abstract and Applied Analysis, 2013 In view of Nevanlinna theory, we study the properties of meromorphic solutions of systems of a class of complex difference equations. Some results obtained improve and extend the previous theorems given by Gao.
Hong-Yan Xu +2 more
doaj +1 more source
Tropical second main theorem and the Nevanlinna inverse problem [PDF]
arXiv, 2023 A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and significantly more straightforward than previously known proofs. The tropical analogue of the Nevanlinna inverse problem
arxiv