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pro vyhledávání: '"Luong, Vu Trong"'
In this paper we study the well-posedness of the evolution equation of the form $u'(t)=Au(t)+Cu(t)$, $t\ge 0$, where $A$ is the generator of a $C_0$- semigroup and $C$ is a (possibly unbounded) linear operator in a Banach space $\mathbb{X}$. We prove
Externí odkaz:
http://arxiv.org/abs/2405.06812
In this paper, by using the spectral theory of functions and properties of evolution semigroups, we establish conditions on the existence, and uniqueness of asymptotic 1-periodic solutions to a class of abstract differential equations with infinite d
Externí odkaz:
http://arxiv.org/abs/2309.02679
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $ D^{\alpha}_Cu(t)=Au(t)+f(t), u(0)=x, 0<\alpha\le1, ( *) $ where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in the Caputo's se
Externí odkaz:
http://arxiv.org/abs/2304.04850
In this paper using a transform defined by the translation operator we introduce the concept of spectrum of sequences that are bounded by $n^\nu$, where $\nu$ is a natural number. We apply this spectral theory to study the asymptotic behavior of solu
Externí odkaz:
http://arxiv.org/abs/2003.05314
Autor:
Van Minh, Nguyen, Luong, Vu Trong
In this paper we study the asymptotic behavior of solutions of fractional differential equations of the form $D^{\alpha}_Cu(t)=Au(t)+f(t)$ on the half line, where $D^{\alpha}_Cu(t)$ is the derivative of the function $u$ in Caputo's sense, $A$ is gene
Externí odkaz:
http://arxiv.org/abs/1910.08609
Autor:
Luong, Vu Trong, Van Minh, Nguyen
We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum of the mono
Externí odkaz:
http://arxiv.org/abs/1807.03826
We study conditions for the abstract linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t), t\ge 0$ to have asymptotic almost periodic solutions, where $F(\cdot )$ is periodic, $f$ is asymptotic almost periodic. The main conditions are sta
Externí odkaz:
http://arxiv.org/abs/1807.03828
Publikováno v:
In Journal of Differential Equations 25 August 2022 329:371-394
Publikováno v:
In Journal of Differential Equations 25 September 2021 296:1-14
Autor:
Luong, Vu Trong1 (AUTHOR), Van Minh, Nguyen2 (AUTHOR) mvnguyen1@ualr.edu
Publikováno v:
Semigroup Forum. Apr2021, Vol. 102 Issue 2, p456-476. 21p.