this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by ...

Matrix representations for a class of Sturm–Liouville problems with eigenparameters contained in the boundary and interface conditions were studied. Given any matrix eigenvalue problem certain type an eigenparameter-dependent condition, this specified condition was constructed. It has been proven that each is equivalent to given problem.

Abstract The present paper deals with a class of third-order differential operators eigenparameter dependent boundary conditions. continuity eigenvalues concerning given parameter is proved. Moreover, the derivative formulas parameters, in particular, condition matrix, are given.

The author studies the inverse scattering problem for a boundary value problem of a generalized one dimensional Schrödinger type with a discontinuous coefficient and eigenparameter dependent boundary condition. The solutions of the considered eigenvalue equation is presented and its scattering function that satisfies some properties is induced. The discrete spectrum is studied and the resolvent...

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using operator-theoretical formulation, transfer the to operator in appropriate Hilbert space. It is proved that self-adjoint. We also give asymptotic formulas of eigenvalues problem. Moreover, Green’s function discussed.

Abstract We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter with ‘a negative number poles’. More precisely, we treat in a unified manner one-dimensional Schrödinger operators either an singularity or condition function at each endpoint and define Darboux-type transformations between such o...