Suppose I want to show that f(t, y) = e^(t - y) satisfies a Lipschitz condition on D = {(t, y): 0 <= t <= 1, -inf < y < inf}.
I want to show |f(t, y1) - f(t, y2)| <= L |y1 - y2|.
Do I just pick arbitrary values for t, y1, y2, and L? E.g. t = 1, y1 = 1, y2 = 0, so
|1 - e| <= L
and I can just say that this satisfies a Lipschitz condition for L = 2?