Inverse spectral problems for nonlinear Sturm-Liouville problems

Abstract

This paper concerns the nonlinear Sturm-Liouville problem -u″(t) + ƒ(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 ƒ(u) by means of the global behavior of the bifurcation branch of the positive solutions in ℝ+ x L2(I).