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I'm not really sure where does this question fit and what title should it bear, but here is my problem:

[itex]\psi(x) \exp (a\psi(x)^2) = C f(x) [/itex]

given a positive definite f(x), find ψ(x) and the constant C, subject to the condition

[itex] \int \psi(x)\, dx = 1 [/itex]

I want to solve this numerically but I'm having a hard time devising a suitable algorithm... is this even a well-posed problem?

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# Non-linear functional problem

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