|Aug24-10, 04:02 PM||#1|
Final condition instead of initial condition
Let's consider a second order differential equation
[tex]f(x,\dot x,\ddot x,t)=0[/tex]
and let's suppose that f satisfies all the conditions of the Cauchy Theorem, i.e. f is such that the equation above with the initial conditions
has an unique solution in a certain neighbourhood of t_0, for every t_0.
My question is, if instead of the two initial conditions above I have an initial and a final condition
under what further conditions on f the solution exists for all x_0 and x_1?
|Aug25-10, 10:54 PM||#2|
The existence depends crucially on the nature of the equation. The solution is, in general, not unique.
|Aug26-10, 02:25 AM||#3|
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