LAUSR

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)=λ2M−iαλK−A$L(\lambda)=\lambda ^{2}M-i\alpha\lambda K-A$, where α>0$\alpha>0$, M and K are self-adjoint operators. Necessary and sufficient conditions are given such that A is self-adjoint.