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 defining a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt's result based on transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x) - tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).
Shahriari, M. (2014). Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions. Computational Methods for Differential Equations, 2(3), 123-139.
MLA
Mohammad Shahriari. "Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions". Computational Methods for Differential Equations, 2, 3, 2014, 123-139.
HARVARD
Shahriari, M. (2014). 'Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions', Computational Methods for Differential Equations, 2(3), pp. 123-139.
VANCOUVER
Shahriari, M. Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions. Computational Methods for Differential Equations, 2014; 2(3): 123-139.
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