Applying numerical discretization my problem leads to: $(A+\mu B)v=c$ where $A$ and $B$ are known real valued square matrices ($N\times N$), $c$ is a known vector, $\mu$ is an unknown parameter (physically should be real), and $v$ is an unknown vector. For what $\mu$ values is the equation solvable?
My idea is to calculate the generalized eigenvalue problem for $A$ and $B$, but I am unsure how to interpret the result.