Geodesic
Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator
Electronic journal of differential equations, Tome 2008 (2008)
In this paper we consider two optimization problems related to the principal eigenvalue of the one dimensional Schrodinger operator. These optimization problems are formulated relative to the rearrangement of a fixed function. We show that both problems have unique solutions, and each of these solutions is a fixed point of an appropriate function.
Classification : 34B05, 34L15
Keywords: Schrödinger equation, principal eigenvalue, minimization, maximization, rearrangements of functions, fixed points 
@article{EJDE_2008__2008__a5,
     author = {Emamizadeh,  Behrouz and Fernandes,  Ryan I.},
     title = {Optimization of the principal eigenvalue of the one-dimensional {Schr\"odinger} operator},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1177.34104},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a5/}
}
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Emamizadeh,  Behrouz; Fernandes,  Ryan I. Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a5/