On the boundary condition resembling Robin boundary condition

Sorry, the minimum problem I simplified is incomplete, so I will give the original problem:

I want to perform a linear stability analysis. The following is the linearized perturbation equation. I try to use the shift-invert method to find eigenvalues.

I learned several example codes solving eigenvalues and found that we can only construct the matrix \mathbf{A} (\mathbf{A}u=\lambda\mathbf{B}u) in a coupling way.

So, when I implemented this problem in FreeFEM++, the boundary condition marked in blue stopped me.

I would greatly appreciate it if you could give me some suggestions on how to deal with this boundary condition. Can the FreeFEM++ solves eigenvalues in a decoupled way?