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- Title
Inverse Sturm-Liouville Problem with Eigenparameter Dependent Boundary and Transmission Conditions.
- Authors
Shahriari, M.
- Abstract
This paper deals with the boundary value problem involving the differential equation ly := -y" + qy = λy subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d + 0) = ay(d - 0), y'(d + 0) = ay'(d - 0) + by(d - 0) at a part d ∈ (0, π), where q(x), a, b are real, q ∈ L²(0, π) and λ is a parameter independent of x. We develop the Hochestadt's result based on transformation operator for inverse Sturm-Liouville problem with eigenparameter dependent boundary and discontinuous conditions. Furthermore, we establish a formula for q(x) - ...(x) in the finite interval, where ...(x) is an analogous function with q(x).
- Subjects
BOUNDARY value problems; DIFFERENTIAL equations; OPERATOR theory; NUMERICAL solutions to Sturm-Liouville equations; GREEN'S functions
- Publication
Azerbaijan Journal of Mathematics, 2014, Vol 4, Issue 2, p16
- ISSN
2218-6816
- Publication type
Article