Electron. J. Diff. Eqns., Vol. 2008(2008), No. 65, pp. 1-11.

Optimization of the principal eigenvalue of the one-dimensional Schrodinger operator

Behrouz Emamizadeh, Ryan I. Fernandes

Abstract:
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.

Submitted January 23, 2008. Published April 28, 2008.
Math Subject Classifications: 34B05, 34L15.
Key Words: Schrodinger equation; principal eigenvalue; minimization; maximization; rearrangements of functions; fixed points

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Behrouz Emamizadeh
Department of Mathematics, The Petroleum Institute
P. O. Box 2533, Abu Dhabi, UAE
email: bemamizadeh@pi.ac.ae
Ryan I. Fernandes
Department of Mathematics, The Petroleum Institute
P. O. Box 2533, Abu Dhabi, UAE
email: rfernandes@pi.ac.ae

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