Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 74, pp. 1-10.

Title: Inverse spectral problems for nonlinear Sturm-Liouville problems

Author: Tetsutaro Shibata (Hiroshima Univ., Higashi-Hiroshima, Japan)

Abstract:
 This paper concerns  the nonlinear Sturm-Liouville problem
 $$
 -u''(t) + f(u(t)) =  \lambda u(t), \quad u(t) > 0, \quad t \in I
 := (0, 1), \quad u(0) = u(1) = 0,
 $$
 where $\lambda $ 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
 $\mathbb{R}_+ \times L^2(I)$.
  
Submitted August 1, 2006. Published May 15, 2007.
Math Subject Classifications: 34B15.
Key Words: Inverse spectral problem; $L^2$-bifurcation diagram;
           logistic equations.