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I am solving a linear dynamical system $X'=A(t) X$, where $t$ is the independent variable and $A(t)$ is a square matrix. Some of the coefficients of $A(t)$ have a discontinuity at a certain value of $t$. I have a heuristic argument as to why the solutions of this system are continuous. Namely, it goes like this: if $X$ is discontinuous, then $X'$ will involve a $\delta$-function, which will not work if I insert it in my system. I am looking for a reference, which would give me theorems I could apply to show that the solutions are continuous.

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  • $\begingroup$ As long as the coefficients are locally integrable, you'll get absolutely continuous solutions. $\endgroup$
    – Christian Remling
    May 27, 2014 at 0:55
  • $\begingroup$ @ChristianRemling Would you mind giving me a reference where this would be discussed? $\endgroup$
    – Gateau au fromage
    May 27, 2014 at 1:01
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    $\begingroup$ Any advanced ODE textbook will work, for example Coddington/Levinson. $\endgroup$
    – Christian Remling
    May 27, 2014 at 1:13
  • $\begingroup$ Please move this question to MSE. $\endgroup$
    – timur
    May 27, 2014 at 6:06

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