How can I solve this integral equation using characteristic values and eigenfunctions?
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$$ f(x)= \int_0^1 e^{|x-t|} f(t) \, dt+x-1 $$
I can't solve it, because I can't find the boundary conditions?
analysisintegral-equations
asked 2011-12-17
user id:21409
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Normally, one uses an iterative technique to solve this. Just start iterating using $x-1$. – 2011-12-17
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Thank you for your comment, however in this exercise I have to use this method (using eigen values) to solve it. Do you know how I can do it? – 2011-12-17
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This is quite interesting as you can consider your integral a linear operator and compute $∫_0^1e^{|x-t|} u(t)dt=\lambda u(x)$. Looking at the answer by Didier, this just becomes $$\lambda u''(x)=3u(x).$$ Taking $\lambda=1$ you are back to the proposed answer. – 2011-12-17