Electron. J. Diff. Eqns., Vol. 2007(2007), No. 74, pp. 1-10.

Inverse spectral problems for nonlinear Sturm-Liouville problems

Tetsutaro Shibata

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.

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Tetsutaro Shibata
Department of Applied Mathematics
Graduate School of Engineering
Hiroshima University
Higashi-Hiroshima, 739-8527, Japan
email: shibata@amath.hiroshima-u.ac.jp

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