Sixth-order Birkhoff regular problems

Asymptotics of the eigenvalues can always be derived for self-adjoint boundary value problems. However, they can also be derived for boundary value problems that fail to be self-adjoint provided that they are Birkhoff regular. A regular sixth-order differential equation that depends quadratically on the eigenvalue parameter $λ$ is considered with classes of separable boundary conditions independent of $λ$ or depending linearly on $λ$. Conditions are given for the problems to be Birkhoff regular.

💡 Research Summary

The paper investigates sixth‑order linear differential eigenvalue problems in which the spectral parameter λ appears quadratically, i.e. the equation is of the form

 −y⁽⁶⁾ + (g₂ y″)″ − (g₁ y′)′ + g₀ y = λ² y,

with real coefficient functions g₀,g₁,g₂∈C⁰, C¹, C² on a finite interval