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Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions | ||
| Computational Methods for Differential Equations | ||
| مقاله 1، دوره 2، شماره 3، مهر 2014، صفحه 123-139 اصل مقاله (499.58 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Mohammad Shahriari* | ||
| University of Maragheh | ||
| چکیده | ||
| 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). | ||
| کلیدواژهها | ||
| Inverse Sturm-Liouville problem؛ Jump conditions؛ Green's function؛ Eigenparameter dependent condition؛ Transformation operator | ||
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