Vol. 92, No. 1, 1981

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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