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A half-inverse problem with eigenparameter dependent boundary conditions. (English) Zbl 1203.34014

Summary: We consider the regular Sturm-Liouville problem

-y '' (x)+q(x)y(x)=λy(x)on[0,1]

with boundary conditions

y(0)cosα+y ' (0)sinα=0,α[0,π)(aλ+b)y(1)=(cλ+d)y ' (1),

where ad-bc>0, c0. We show that if q(x) is prescribed on the half interval [1 2,1], then a single spectrum suffices to determine q(x) on [0,1], the boundary condition at x=0 and “the asymptotic” boundary condition at x=1.

34A55Inverse problems of ODE
34B24Sturm-Liouville theory