Vol. 92, No. 1, 1981

Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Positive solutions and spectral properties of second order elliptic operators

Walter Allegretto

Vol. 92 (1981), No. 1, 15–25

Let l denote a second order elliptic expression in divergence form and with coefficients defined in an exterior domain. In this paper it is shown that, under suitable conditions, the equation lv = 0 has an a.e. positive generalized solution v defined in a neighborhood of infinity. This is done under weaker conditions on the coefficients of l than was previously required. It is then shown that the existence of such a v implies the finiteness of the negative spectrum of operators naturally associated with l.

Mathematical Subject Classification 2000
Primary: 35J15
Secondary: 35P05
Received: 11 April 1979
Published: 1 January 1981
Walter Allegretto