EUDML

The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.

Periodic solutions for some nonautonomous $p (t)$ -Laplacian Hamiltonian systems

Liang Zhang; X. H. Tang — 2013

Applications of Mathematics

In this paper, we deal with the existence of periodic solutions of the $p (t)$ -Laplacian Hamiltonian system $\{\begin{matrix} \frac{d}{d t} (| \dot{u} (t) |^{p (t) - 2} \dot{u} (t)) = \nabla F (t, u (t)) a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0 . \end{matrix}$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.

A simple sufficient descent method for unconstrained optimization.

Zhang, Ming-Liang; Xiao, Yun-Hai; Zhou, Dangzhen — 2010

Mathematical Problems in Engineering

Ramanujan's identities for eta-functions.

B.C. Berndt; Liang-Cheng Zhang — 1992

Mathematische Annalen

On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1

Liang-Cheng Zhang; Jonathan Gordon — 1991

Acta Arithmetica

OD-characterization of almost simple groups related to $L_{2} (49)$

Liang Cai Zhang; Wu Jie Shi — 2008

Archivum Mathematicum

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_{2} (49)$ . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_{2} (49)$ except $L_{2} (49) \cdot 2^{2}$ . Also, we prove that if $M$ is an almost simple group related to $L_{2} (49)$ except $L_{2} (49) \cdot 2^{2}$ and $G$ is a finite group such that $| G | = | M |$ and $Γ (G) = Γ (M)$ , then $G ≅ M$ .

Disjoint hypercyclic powers of weighted translations on groups

Liang Zhang; Hui-Qiang Lu; Xiao-Mei Fu; Ze-Hua Zhou — 2017

Czechoslovak Mathematical Journal

Let $G$ be a locally compact group and let $1 \leq p < \infty .$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^{p} (G)$ in terms of the weights. Sufficient and...