On Some Quadratic Eigenvalue Problems

In a number of second- and fourth-order boundary value problems the spectral parameter \(\lambda \) appears quadratically as well as linearly. The paper deals with eigenvalue problems of this type. Here, an approach for linearization is proposed for both second- and fourth-order problems. By suitable substitution, a variational system is obtained in which spectral parameter \(\lambda \) appears only linearly but not quadratically. Theoretical and computational aspects are considered. Combining linearization and the mixed method for fourth-order problems is also discussed. Finally, numerical results are presented.