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Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales
Existence of \(\Psi\)-bounded solutions for linear differential systems on time scales
en
en
In this paper, we define \(\Psi \)-boundedness on time scales and we present necessary and sufficient conditions for the existence of at least one \(\Psi\)-bounded solution for the linear non-homogeneous matrix system \(x^{\Delta}=A(t)x + f(t)\), where f(t) is a \(\Psi\)-bounded matrix valued function on \({T}\) assuming that \(f\) is a Lebesgue \(\Psi\)-delta integrable function on time scale \({T}\). Finally we give a result in connection with the asymptotic behavior of the \(\Psi\)-bounded solutions of this system.
1
13
Kasi Viswanadh V.
Kanuri
USA
vis.kanuri@gmail.com
R.
Suryanarayana
Department of Mathematics
Vishnu Institute of Technology
India
bhavyarsn@gmail.com
K. N.
Murty
Department of Applied Mathematics
Andhra University
India
nkanuri@hotmail.com
\(\Psi\)-bounded
\(\Psi\)-integrable
Lebesgue \(\Psi\)-delta integrable
Article.1.pdf
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Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems
Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems
en
en
Assume that \((W, g_{1,\infty})\) is a
nonautonomous discrete dynamical system given by sequences \((g_{m})_{m=1}^{\infty}\) of continuous maps on the space \((W,d)\).
In this paper, it is proven that if \(g_{1, \infty}\) is topologically weakly mixing and satisfies that
\(g_{1}^{n}\circ g_{1}^{m}=g_{1}^{n+m}\) for any \(n,m\in\{0,1,\ldots\}\), then it is distributional chaos in a sequence.
This result extends the existing one.
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20
Yu
Zhao
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
datom@189.cn
Risong
Li
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Hongqing
Wang
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
wanghq3333@126.com
Haihua
Liang
School of Mathematics and Computer Science
Guangdong Ocean University
P. R. China
lhhlucy@126.com
Chaotic in the sense of Devaney
topologically transitive
sensitive
nonautonomous discrete dynamical systems
distributional chaos in a sequence
Article.2.pdf
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