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August 9th, 2010, 11:16 AM  #1 
Newbie Joined: Aug 2010 Posts: 8 Thanks: 0  A 1st order nonlinear ODE
I am proving a theorem and I need to understand the asymptotic behavior of the solution to a differential equation, which probably can't be solved explicitly. Let and , , be the solution to the initial value problem where is a bounded function (which doesn't depend on ). The conjecture is that as , where a, b are constants. I actually think is real analytic in . The existence of the constant follows easily since the function is decreasing and bounded below, as decreases to zero. I don't know how to show that exists. Any help or idea is appreciated. 
August 14th, 2010, 12:05 PM  #2 
Member Joined: Aug 2007 Posts: 42 Thanks: 4  Re: A 1st order nonlinear ODE
I am not sure your solutions must be defined up to x=1. Also, for smooth but not analytic psi, the expansion for u(1) is not valid.

August 15th, 2010, 04:44 PM  #3  
Newbie Joined: Aug 2010 Posts: 8 Thanks: 0  Re: A 1st order nonlinear ODE Quote:
 
August 15th, 2010, 04:48 PM  #4 
Newbie Joined: Aug 2010 Posts: 8 Thanks: 0  Re: A 1st order nonlinear ODE
Actually I am not sure about the error term. I will be equally happy if anyone can prove or disprove In other words, the question is whether there exist constants a, b such that Any help is appreciated. 
August 17th, 2010, 09:16 AM  #5  
Newbie Joined: Aug 2010 Posts: 8 Thanks: 0  Re: A 1st order nonlinear ODE Quote:
 

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