Results 31 to 40 of about 369 (181)

Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems

Journal of Function Spaces, 2016
Estimating the growth of meromorphic solutions has been an important topic of research in complex differential equations. In this paper, we devoted to considering uniqueness problems by estimating the growth of meromorphic functions.
Jianming Qi, Fanning Meng, Wenjun Yuan
doaj   +1 more source

Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations [PDF]

Mathematica Bohemica
Firstly we study the growth of meromorphic solutions of linear difference equation of the form A_k(z)f(z+c_k)+\cdots+A_1(z)f(z+c_1)+A_0(z)f(z)=F(z), where $A_k(z),\ldots,A_0(z)$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_i$
Abdelkader Dahmani, Benharrat Belaïdi
doaj   +1 more source

The Benjamin–Ono Equation in the Zero‐Dispersion Limit for Rational Initial Data: Generation of Dispersive Shock Waves

Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.
ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone, Louise Gassot, Patrick Gérard, Peter D. Miller   +3 more
wiley   +1 more source

Oscillation results on meromorphic solutions of second order differential equations in the complex plane

Electronic Journal of Qualitative Theory of Differential Equations, 2010
The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form $f^{''}+A(z)f=0$ where $A$ is meromorphic in the complex plane. We improve and extend some oscillation
Ting-Bin Cao, Lei-Min Li
doaj   +1 more source

The Mathematical History Behind the Granger–Johansen Representation Theorem

Oxford Bulletin of Economics and Statistics, Volume 88, Issue 4, Page 587-602, August 2026.
ABSTRACT When can a vector time series that is integrated once (i.e., becomes stationary after taking first differences) be described in error correction form? The answer to this is provided by the Granger–Johansen representation theorem. From a mathematical point of view, the theorem can be viewed as essentially a statement concerning the geometry of ...
Johannes M. Schumacher
wiley   +1 more source

On growth of meromorphic solutions for linear difference equations with meromorphic coefficients [PDF]

Advances in Difference Equations, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Uniform Asymptotics of Solutions of Second-Order Differential Equations with Meromorphic Coefficients in a Neighborhood of Singular Points and Their Applications

Mathematics, 2022
In this paper, we consider the problem of obtaining the asymptotics of solutions of differential operators in a neighborhood of an irregular singular point.
Maria V. Korovina, Hovik A. Matevossian
doaj   +1 more source

Quasiconformal folding—a review of ‘Models for the Eremenko–Lyubich class'

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We review the paper ‘Models for the Eremenko–Lyubich class’ by Bishop, which appeared in the Journal of the London Mathematical Society in 2015, the first of two LMS papers for which Bishop received the LMS Senior Berwick Prize in 2024. This is one of a series of papers where Bishop introduced his new technique of quasiconformal folding, which
Philip J. Rippon
wiley   +1 more source

An EZ${\mathcal {E}\mathcal {Z}}$‐structure for the mapping class group

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We construct a boundary for the mapping class group Mod(S)${\rm Mod}(S)$ of a surface S$S$ of finite type. The action of Mod(S)${\rm Mod}(S)$ on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of an EZ${\mathcal {E}\mathcal {Z}}$‐structure for Mod(S)${\rm Mod}(S)$.
Ursula Hamenstädt
wiley   +1 more source

New exact solutions of the sixth-order thin-film equation with complex method

Partial Differential Equations in Applied Mathematics, 2021
By the Wiman–Valiron theory and the complex method, we prove that all meromorphic solutions of the fifth-order ODE unu′′′′′−cu=0belong to W, and obtain several new solutions of the sixth-order thin-film equation comparing to the opening literature.
Guoqiang Dang
doaj   +1 more source