Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Nonlinear Bessel-type ODE

  1. Jul 12, 2016 #1
    Is there an approach to the following 2nd order nonlinear ODE?
    xy'' + 2 y' = y^2 - k^2
    I am interested in learning how to analyze for asymptotic behavior, proof of existence, etc.
  2. jcsd
  3. Jul 18, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Jul 19, 2016 #3
    I can transform this equation into a more standard form: $$u^2 z_{uu} - u z_u + u^2 z = z^2.$$ I found a paper that kind of answers my question: http://www.sciencedirect.com/science/article/pii/0898122196000569

    It would be nice to show that the solution is Lyapunov stable about z(u=0) = 0... Anyone know how to do that?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted