An inverse nodal problem for two-parameter Sturm–Liouville systems

We consider uniqueness and reconstruction of the potentials qj L1, and of the (separated) boundary condition parameters, from a dense sequence of nodal points for a two-parameter system of Sturm?Liouville equations linked by the eigenvalue pairs (?, ?). Under the 'right definiteness' condition a1(t1)b2(t1) ? b1(t1)a2(t2) > 0 for all t1, t2, we show that a single sequence of nodal points for each j = 1, 2, one point for each eigenfunction yjk, k = 1, 2, ..., suffices for our purposes.