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Global solution to inhomogeneous Bernoulli ODE

  1. Feb 2, 2013 #1
    Hi everyone,

    I have an inhomogeneous Bernoulli type ODE given by

    [itex] u'(t) = \kappa u(t) + \ell(t) u^{\gamma}(t) + v(t),\ \ \ u(T)=b>0,...(1) [/itex]

    where [itex] t\in[0,T],\ \ \gamma\in (0,1) [/itex].

    My concern is that how to prove the existence and uniqueness of the solution u(t) for all [itex]t\in [0,T] .[/itex] Thanks very much.
     
  2. jcsd
  3. Feb 4, 2013 #2

    HallsofIvy

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    As long as l(t) and v(t) are "Lipschitz" ("differentiable" is sufficient but not necessary) on [0, 1], that follows from the elementary "existance and uniqueness" theorem for intial value prolems of the for equations of the form y'= f(t, y).
     
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