Geodesic
Inverse spectral problems for nonlinear Sturm-Liouville problems
Electronic journal of differential equations, Tome 2007 (2007)
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__a30,
     author = {Shibata,  Tetsutaro},
     title = {Inverse spectral problems for nonlinear {Sturm-Liouville} problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1140.34307},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a30/}
}
TY  - JOUR
AU  - Shibata,  Tetsutaro
TI  - Inverse spectral problems for nonlinear Sturm-Liouville problems
JO  - Electronic journal of differential equations
PY  - 2007
VL  - 2007
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a30/
LA  - en
ID  - EJDE_2007__2007__a30
ER  - 
%0 Journal Article
%A Shibata,  Tetsutaro
%T Inverse spectral problems for nonlinear Sturm-Liouville problems
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a30/
%G en
%F EJDE_2007__2007__a30
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__a30/