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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