Geodesic
Inverse spectral problems for nonlinear Sturm-Liouville problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\mathbb{R}_+ \times L^2(I)$.
Classification : 34B15
Keywords: inverse spectral problem, $L^2$-bifurcation diagram, logistic equations 
@article{EJDE_2007__2007__a230,
     author = {Shibata, Tetsutaro},
     title = {Inverse spectral problems for nonlinear {Sturm-Liouville} problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a230/}
}
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Shibata, Tetsutaro. Inverse spectral problems for nonlinear Sturm-Liouville problems. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a230/