Does a Solution Exist for a Discontinuous Differential Equation?

[yifli]

Given a differential equation dy/dt = F(t,y), can anyone give me an example that shows no solution exists if F(t,y) is discontinuous?

Thanks

 

[micromass]

Hi yifli!

Check out Darboux's theorem. It says that the derivative of every function have the intermediate value property.
So, if you can find a function f without that property, then you'd know that

y^\prime=f(t)

has no solutions. So, try to find a function without that property...