Class Of Matrix Problems Research Articles

Matrix representations of fourth-order boundary value problems with coupled or mixed boundary conditions

An equivalence between a class of regular self-adjoint fourth-order boundary value problems with coupled or mixed boundary conditions and a certain class of matrix problems is investigated. Such an equivalence was previously known only in the second-order case and fourth-order case with separated boundary conditions.

Matrix representations of fourth order boundary value problems with periodic boundary conditions

We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same eigenvalues. Such an equivalence is considered with the special coupled boundary conditions, i.e. periodic boundary conditions.

Matrix representations of Sturm–Liouville problems with eigenparameter-dependent boundary conditions

We show that a class of regular self-adjoint Sturm–Liouville problems with eigenparameter-dependent boundary conditions are equivalent to a certain class of matrix problems. Equivalent here means that they have exactly the same eigenvalues.

Equivalence of Fourth Order Boundary Value Problems and Matrix Eigenvalue Problems

We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same spectrum.

Matrix representations of fourth order boundary value problems with finite spectrum

We show that a class of regular self-adjoint fourth order boundary value problems is equivalent to a certain class of matrix problems. Equivalent here means that they have exactly the same eigenvalues. Such an equivalence was previously known only in the second order case.