MONOTONICITY OF EIGENVALUES

LEON GREENBERG

lng@math.umd.edu

Department of Mathematics

University of Maryland

College Park

Maryland MD 20742 , USA

University of Maryland

College Park

Maryland MD 20742 , USA

For
, consider the family of Sturm-Liouville
problems:

where , and . The Sturm-Liouville problem (1) has a sequence of eigenvalues: . A well known Sturmian property states that if the second boundary condition (1c) is a Dirichlet condition (i.e. if ) then the eigenvalues are strictly decreasing functions of . We ask the question: Does any vestige of this property remain true if ? The answer is yes.

EPSRC Gregynog Workshop, 21-26 July 2002