Does this linear integral equation defined on $[-a,a]$ have any nonconstant solution? I am more interested in the exsistence of solution rather than the solution itself. The boundary condition has two cases:
Case $\bf(1)$ : $~y(-a)=y(a)=b~~$ and
Case $\bf(2)$ : $~-y(-a)=y(a)=c~$. $$\int_{-a}^{a}{ \frac{y(x)-y(x')}{(x-x')^2} ~~d x'}=0$$
I feel the solution, it exists at all, could be something simple. But I am not sure how to (dis)prove the exsistence or solve it.