Inverse spectral problems for differential pencils with the turning point in the finite interval (Q1689278)

The inverse spectral problem is studied for the boundary value problem \(L\): \[ y''+(\rho^2r(x)+i\rho q(x)+p(x))y=0,\; x\in(0,1), \] \[ y'(0)-(ih\rho+h_0)y(0)=y'(1)+(iH\rho+H_0)y(1)=0, \] where \(r(x)=\mathrm{sign}(x-a),\) \(a\in(0,1),\) and \(h\neq\pm 1,\pm i\). By the method of spectral mappings it is proved that the specification of the Weyl-type function uniquely determines \(L\).