Find a non-trivial solution in the first quadrant for:

Hint: Can you think of a trial function of two parameters that would make the right side converge?

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- October 18th 2009, 06:46 AM #1

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- October 19th 2009, 12:58 PM #2

- October 19th 2009, 01:45 PM #3

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- October 20th 2009, 03:01 AM #4
That was me being careless, trying to do something in a hurry late at night (excuses, excuses...). The equation should have been . That has no real solutions for positive and . But it does have complex solutions with positive real parts (which are necessary for the integral to converge), for example . Unless I'm still making silly mistakes, that should give a complex solution to the problem. I don't have time to check it now, but I suppose that the real part of that ought to give a real solution.

__Spoiler__:

- October 20th 2009, 05:35 AM #5

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That's the right relationship between a and b. So there are only complex solutions. So if the operator is linear:

with a solution, then won't u and v be independent solutions as well?

Anyone care to explain the plot? Where are the solutions in complex a-b space?