Suppose we have a second order eigenvalue problem with kinda special nonlocal condition.

The equation takes form of a simple harmonic oscillator ( neither driven nor damped) on (0,Pi), but its not necessary, conditions are main deal.

First one is something like y(0) = 0,this is ok, but second one is , lets simplify it, " measure of positive semi-wave of solution = measure of negative semi-wave of solution" (in fact its measure with parameters for both semiwaves that are, in general, not equal). Measure = area under curve, so there definite integral takes place.

To be clear, im not asking for code, i just wanna know whether is possible to deal with integral conditions with Mathematica.

Thanks