Let F be continuous and satisfy
|F(x,y_2) - F(x,y_1)| ≦ k(x)|y_2 - y_1|
on the strip 0 < x < a.
a
Show that, if the improper integral ∫k(x)dx is finite, then y'=F(x,y) has
0
at most one solution satisfying y(0)=0.
[Hint: Define σ(x) = [y_2(x) - y_1(x)]^2 and show that σ(x) possesses
certain decreasing property.]
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