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Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions. (English) Zbl 0960.34010
Theorems analogous to those of {\it V. A. Marchenko} [Dokl. Akad. Nauk SSSR, n. Ser. 72, 457-460 (1950; Zbl 0040.34301)] and {\it H. Hochstadt} [J. Differ. Equations 17, 220-235 (1975; Zbl 0266.34027)] are proved for the boundary value problem $$ -(p(x)y')'+q(x)y=\lambda r(x)y,\quad 0<x<1, $$ $$ y(0)\cos\alpha+y'(0)\sin\alpha=0,\quad (a\lambda+b)y(1)=(c\lambda+d)y'(1), $$ where $r(x), p(x)\in C^1$ are positive with absolutely continuous derivatives, $q(x)\in L^1, \alpha, a, b, c, d$ are real, $c\ne 0,$ and $ad-bc>0.$ The case of two eigenparameter-dependent boundary conditions is also considered.

34B07Linear boundary value problems with nonlinear dependence
34A55Inverse problems of ODE
34L05General spectral theory for OD operators
34B24Sturm-Liouville theory
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