Nonseparated Boundary Conditions Research Articles

Reduction of Linear Two-point Boundary Value Problems with Non-separable Boundary Conditions to Cauchy Systems

It is shown that some linear two-point boundary value problems subject to non-separable boundary conditions may be reduced to initial value problems.

Second-order equations with two point and integral boundary conditions

The existence of eigenvalues for second-order linear equations with a combination of integral and nonseparated boundary conditions is proved. This generalizes some recent results, due to Etgen and Tefteller, and W. M. Whyburn.

The inverse problem for differential operators of second order with regular boundary conditions

This paper is devoted to the proof of the unique solvability of the inverse problem for second-order differential operators with arbitrary regular nonseparable boundary conditions. It is shown that the operator can be recovered from three of its spectra. As a special case, the well-known reconstruction of the Sturm-Liouville operator is accomplished.

An initial-value method for the eigenvalue problem for differential equations with nonseparated boundary conditions

An initial-value technique is presented for the calculation of the characteristic lengths and characteristic functions of linear second-order ordinary differential equations subject to general nonseparated boundary conditions. Numerical examples are presented which demonstrate the efficacy of the method.

An initial value method for the eigenvalue problem for systems of ordinary differential equations

An initial value method is presented for the calculation of characteristic lengths and characteristic functions of systems of ordinary differential equations. Very general nonseparated boundary conditions can be handled and the equations tend to be quite stable numerically. Numerical examples are presented which demonstrate the efficacy of the method.