A regular fourth-order differential equation that depends quadratically on the eigenvalue parameter $\lambda$ is considered with classes of separable boundary conditions independent of $\lambda$ or depending on $\lambda$ linearly. Conditions are given for the problems to be Birkhoff regular.
"Fourth-order Birkhoff regular problems with eigenvalue parameter dependent boundary conditions,"
Turkish Journal of Mathematics: Vol. 40:
4, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss4/15