Rearrangements of functions and lower bounds for eigenvalues of differential equations

Abstract

We are concerned with eigenvalue problems of the form

subject to boundary conditions in the first case and in the second case. The eigenvalues of these systems depend on the coefficients and we denote them accordingly and . We introduce some new kinds of rearrangements of functions and relate them to those given by B. Schwarz [19]. Our main results are that if ≦0 then

and if then

This research was partially supported by NSF grant GP-14428.

This research was partially supported by NSF grant GP-14428.

Notes

This research was partially supported by NSF grant GP-14428.

Additional information

Notes on contributors

R. P. Gilbert