Re: How to solve this type of equation in Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg59999] Re: How to solve this type of equation in Mathematica?
- From: Jeffrey Lyons <not-me at nospam.net>
- Date: Sun, 28 Aug 2005 03:07:35 -0400 (EDT)
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On Sat, 27 Aug 2005 08:15:35 +0000 (UTC), robert.dodier at gmail.com wrote: >It looks to me like this isn't strong enough >to yield a unique solution (or even a solution in >a well-known class). > >If you replace f by A f where A is a constant >you get A times \int_P^{\infty} (x + P) f(x) dx. >So let f be any function s.t. the integral is defined >and not equal to zero. (I believe that's a fairly >large class.) If the integral I is not equal to 1, >replace f by f/I and that's a solution, >if I'm not mistaken. > >The equation is an example of an integral equation, >so you might be able to find more info under that >heading. Sorry that I can't be more helpful. > >Robert Dodier Robert, thanks so much for your interest in this problem. Your solution, replacing f(x) with f(x)/I if f is not equal to 1, still does not prove there is a solution for f(x). For all the solutions of this type that I can think of the new f(x) is now a function of both x and P, ie f(x, P). For example: f(x,P) =0.6666 * x^ (-3) * P^(-1) is a solution. What I need is a an f that is only a function of the variable "x". Can it be proven that there is/(is not) a solution to my equation if f is only a function of the variable x and not a function of "P"? Again any assistance would be appreciated.
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