No abstract

No abstract

Fourth order eigenvalue problems with periodic and separated boundary conditions are considered. One of the separated boundary conditions depends linearly on the eigenvalue parameter λ. These problems can be represented by an operator polynomial L(λ) = λ 2 M -iαλK -A, where α > 0, M and K are self-adjoint operators.Necessary and sufficient conditions are given such that A is self-adjoint.MSC: Primary 34B07; secondary 34B08; 47E05

A regular fourth-order differential equation that depends quadratically on the eigenvalue parameter λ is considered with classes of separable boundary conditions independent of λ or depending on λ linearly. Conditions are given for the problems to be Birkhoff regular.

A regular fourth order differential equation with λ-dependent boundary conditions is considered. For four distinct cases with exactly one λ-independent boundary condition, the asymptotic eigenvalue distribution is presented.