In this paper, a Sturm–Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that coefficients can be uniquely determined by dense set nodal points. Moreover, we give an algorithm for reconstruction potential function and other in conditions.

This paper concerns the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0, where λ is a positive parameter. We try to determine the nonlinear term f(u) by means of the global behavior of the bifurcation branch of the positive solutions in R+ × L2(I).