I am working on the following problem and I am completely stuck:
Show that the eigenvalue problem $$ -u''+4\pi^{2}\int_{0}^{1} u(x)\,dx=\lambda\,u $$ with $u(0)=u(1)$ and $u'(0)=u'(1)$ has $\lambda=4\pi^2$ an eigenvalue of multiplicity $3$. I don't how to deal with the integral term. No solutions please but any hint will be much appreciated.