Uniqueness of the nonlinear term of a boundary value problem from the first bifurcating branch (Q1269355)

The author studies the inverse problem of recovering the nonlinearity \(g\in C^1(\mathbb{R})\) with \(g(0)=g'(0)=0\) in the boundary value problem \[ u''+\lambda u-q(x)u= g(u), \quad u'(0)=u(1)=0, \] from its first bifurcation branch.