# Convergence results for solutions of a first-order differential equation

Volume 6, Issue 1, pp 18--28
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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.

•  28A20
•  28A33
•  46E30
•  46N10

### References

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