On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem. (2nd July 2020) - Liu, Xiaoyun
Abstract : An m -dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence y n j, r x, λ n j, r 2 j = 1 ∞ of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix Q x and A are simultaneously diagonalizable by the same unitary matrix U . Subsequently, some multiplicity results of eigenvalues are obtained.