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By
Sun, Peng
1 Citations
We show that a flow or a semiflow with a weak form of reparametrized gluing orbit property has positive topological entropy if it is not minimal.
By
Almahalebi, Muaadh; Chahbi, Abdellatif
1 Citations
The aim of this paper is to introduce and solve the
pradical functional equation
$$f\left( {\sqrt[p]{{x^p + y^p }}} \right) = f\left( x \right) + f\left( y \right),p \in \mathbb{N}_2 .$$
We also state an analogue of the fixed point theorem [12, Theorem 1] in 2Banach spaces and investigate stability for this equation in 2Banach spaces.
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By
Liao, Yongkai
1 Citations
This paper is concerned with the largetime behavior of solutions to the Cauchy problem of a onedimensional viscous radiative and reactive gas. Based on the elaborate energy estimates, we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t) and W(t) introduced by Liao and Zhao [J. Differential Equations, 2018, 265(5): 2076–2120]. Our results also improve upon the results obtained in Liao and Zhao [J. Differential Equations, 2018, 265(5): 2076–2120].
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By
Ji, Lina; Zheng, Xiangqi
For continuousstate branching processes in Lévy random environments, the recursion of nmoments and the equivalent condition for the existence of general fmoments are established, where f is a positive continuous function satisfying some standard conditions.
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By
Editorial Office of Acta Mathematica Scientia
The EditorinChief has retracted this article [1], because one of the Editorial Board Mem bers pointed out that Lemma 3.5 in [1] has an uncorrectable gap which can only be true when n = 1, 2, 3, indicating that the major theorem 1.1 in [1] is only a special case of Theorem 1 in [2], and Theorem 1.2 in [1] is only a trivial result in [3]. The author refused to retract the article [1] in his first response to editors and claimed that the existing gap is unimportant. The author has not responded again by the deadline clearly informed to the author.
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By
Wang, Jing; Li, Yonggang; Sun, Huafei
Suppose that A and B are two positivedefinite matrices, then, the limit of (A^{p/2}B^{p}A^{p/2})^{1/p} as p tends to 0 can be obtained by the well known LieTrotter formula. In this article, we generalize the usual product of matrices to the Hadamard product denoted as * which is commutative, and obtain the explicit formula of the limit (A^{p} * B^{p})^{1/p} as p tends to 0. Furthermore, the existence of the limit of (A^{p} * B^{p})^{1/p} as p tends to +∞ is proved.
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By
Liang, Zaitao; Yang, Yanjuan
In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a wellknown fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.
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By
Wang, Shu; Jiang, Limin
In this article we study quasineutral limit and the initial layer problem of the driftdiffusion model. Different from others studies, we consider the physical case that the mobilities of the charges are different. The quasineutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multiscaling asymptotic expansions.
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By
Huang, Jianjun; Jiang, Zhenglu
This article extends the results of Arkeryd and Cercignani [6]. It is shown that the Cauchy problem for the relativistic Enskog equation in a periodic box has a global mild solution if the mass, energy and entropy of the initial data are finite. It is also found that the solutions of the relativistic Enskog equation weakly converge to the solutions of the relativistic Boltzmann equation in L^{1} if the diameter of the relativistic particle tends to zero.
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By
Hu, Zejun; Yin, Jiabin
Associated with an immersion φ : S^{3} → ℂP^{3}, we can define a canonical bundle endomorphism F : TS^{3} → TS^{3} by the pull back of the Kahler form of ℂP^{3}. In this article, related to F we study equivariant minimal immersions from S^{3} into ℂP^{3} under the additional condition (∇_{X}F)X = 0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant nonminimal immersion φ: S^{3} → ℂP^{3} satisfying (∇_{X}F)X = 0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.
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