1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Diff Eq. Proving the existence of a unique solution

  1. Mar 14, 2012 #1
    Can somebody help me out here?

    Consider y'(t) = y(t)[a(t) - b(t)y(t)] where a,b : (-infinite, +infinite) → (0, +infinity)
    and there exists M>0 such that: (1/M) ≤ a(t), b(t) ≤ M, for all t in the reals

    Claim: There exists a unique positive solution Phi(t) defined for all t in the reals in which there exists an m>0 such that: (1/m) ≤ Phi(t) ≤ m. (i.e. Phi(t) is bounded and bounded away from zero)

    note that a(t) and b(t) are not necessarily periodic.

    Prove the claim true or false.

    Any help would be tremendously appreciated. I'm practically dying over this one.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted