Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I need to use the Gronwall inequality to discuss existence/uniqueness of the solution to the initial value problem:

x'(t)=xsin(tx) + t with initial condition x(t_{0}) = x_{0}.

I can convert this into integral form

[tex]x(t) = x_0 + \int\limits_{t_0}^{t} xsin(sx) + s ds[/tex]

Which of course can reduce to

[tex]x(t) = x_0 + \frac{t^2}{2} - \frac{t_0^2}{2} + \int\limits_{t_0}^{t} xsin(sx) ds[/tex]

But I'm unsure of how to progress from here. Also any links to other good places to study this material would help.

Thank you.

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

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

# Using Gronwall Inequality to Prove Uniqueness/Existence

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Using Gronwall Inequality | Date |
---|---|

I Ode using Fourier Transform | Jan 2, 2018 |

I Using Complex Numbers to find the solutions (simple Q.) | Dec 29, 2017 |

A 2nd Order PDE Using Similarity Method | May 14, 2017 |

I What method can be used to solve this pde? | Apr 4, 2017 |

PDE with an inequality constrain | Oct 20, 2012 |

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