Unsolved problems in differential equations?

[jonjacson]

¿unsolved problems in differential equations?

Hi, I would like to talk with you about the modern lines of investigation about differential equations ( ode,pde...) , which are the most interesting unsolved questions, ecuations to solve, general tools for solving differential equations ...


I know we have learned a lot, but still there is a lot of work to do .

 

[LCKurtz]

I know a professor who when asked after a colloquium talk to state one of the most important unsolved problems in differential equations stepped to the chalkboard and wrote:

$$y' = f(x,y)$$

and sat down.

 

[MathematicalPhysicist]

Yes most equations can't be solved analyticly...

 

[jonjacson]

I know a professor who when asked after a colloquium talk to state one of the most important unsolved problems in differential equations stepped to the chalkboard and wrote:

$$y' = f(x,y)$$

and sat down.

He should be more precise, I think that you could demonstrate the exixtence and uniqueness of a solution using Picard's method.

Perhaps he was asking for a general method to find the solution?

 

[g_edgar]

Here's one with a prize ...

http://www.claymath.org/millennium/Navier-Stokes_Equations/