# 2008-12 Finding eigenvalues and eigenvectors

Find all real numbers $$\lambda$$ and the corresponding functions $$f$$ such that the equation

$$\displaystyle \int_0^1 \min(x,y) f(y) \,dy=\lambda f(x)$$
has a non-zero solution $$f$$ that is continuous on the interval [0,1].

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