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]. 

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations!

Here is his Solution of Problem 2008-12.