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Sep 7, 2012 at 17:29 comment added Elena Yudovina What I actually wanted is "$f$ piecewise linear, but discontinuous, i.e. with jumps between the pieces". (E.g., $f(X)=I[X>0]$.) This particular example gives multiple solutions from $X(0) = 0$ if I only require $X'(t) = f(X)$ whenever the two-sided derivative exists, but forcing the right derivative to be $f(X)$ everywhere squashes them out.
Sep 7, 2012 at 17:22 vote accept Elena Yudovina
Sep 7, 2012 at 15:37 history edited Thomas Richard CC BY-SA 3.0
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Sep 7, 2012 at 15:24 history edited Thomas Richard CC BY-SA 3.0
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Sep 7, 2012 at 15:18 history answered Thomas Richard CC BY-SA 3.0