Equivalence of fourth order boundary value problems and matrix eigenvalue problems (Q1936948)

The authors establish equivalent relations between a class of regular self-adjoint fourth-order linear boundary value problems and a class of matrix problems. More precisely, they show that (i) for any boundary value problem in the first class, there exists a matrix problem in the second class with exactly the same spectrum; (ii) for any matrix problem in the second class, there exists a boundary value problem in the first class with exactly the same spectrum. This work is an extension of an earlier work by Kong, Wu, and Zettl in 2001 and that by Kong, Volkmer, and Zettl in 2009 for second-order problems, and is a follow-up of the authors' work on fourth-order problems.