Convergence results for solutions of a first-order differential equation
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Authors
Liviu C. Florescu
- Faculty of Mathematics, ''Al. I. Cuza'' University, Carol I, 11, 700506, Iaşi, Romania.
Abstract
We consider the first order differential problem:
\[
(P_n)
\begin{cases}
u'(t) = f_n(t, u(t)),\,\,\,\,\, \texttt{for almost every} \quad t \in [0, 1],\\
u(0) = 0.
\end{cases}
\]
Under certain conditions on the functions \(f_n\), the problem \((P_n)\) admits a unique solution \(u_n \in W^{1;1}([0; 1];E)\).
In this paper, we propose to study the limit behavior of sequences \((u_n)_{n\in \mathbb{N}}\) and \((u'_n)_{n\in \mathbb{N}}\), when the sequence
\((f_n)_{n\in \mathbb{N}}\) is subject to different growing conditions.
Share and Cite
ISRP Style
Liviu C. Florescu, Convergence results for solutions of a first-order differential equation, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 1, 18--28
AMA Style
Florescu Liviu C., Convergence results for solutions of a first-order differential equation. J. Nonlinear Sci. Appl. (2013); 6(1):18--28
Chicago/Turabian Style
Florescu, Liviu C.. "Convergence results for solutions of a first-order differential equation." Journal of Nonlinear Sciences and Applications, 6, no. 1 (2013): 18--28
Keywords
- Tight sets
- Jordan finite-tight sets
- Young measure
- fiber product
- Prohorov's theorem.
MSC
References
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