Let's consider a second order differential equation(adsbygoogle = window.adsbygoogle || []).push({});

[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

[tex]x(t_0)=x_0\qquad\dot x(t_0)=v_0[/tex]

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

[tex]x(t_0)=x_0\qquad x(t_1)=x_1[/tex]

under what further conditions on f the solution exists for all x_0 and x_1?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Final condition instead of initial condition

Loading...

Similar Threads for Final condition instead | Date |
---|---|

A Applying boundary conditions on an almost spherical body | Feb 15, 2018 |

I Boundary Conditions for System of PDEs | Jan 17, 2018 |

Final velocity of a rocket launching to space | Sep 29, 2014 |

Maple integration: 8 equations using final values of first 4 to solve second set | Feb 23, 2011 |

**Physics Forums - The Fusion of Science and Community**