Oscillation criteria for elliptic equations

Velmer B. Headley and Charles Andrew Swanson

Vol. 27 (1968), No. 3, 501–506

DOI: 10.2140/pjm.1968.27.501

Abstract

Conditions on the coefficients of a linear elliptic partial differential equation will be obtained which are sufficient for the equation to be oscillatory in certain unbounded domains. The criteria obtained in the first three theorems involve integrals of suitable majorants of the coefficients while the criterion in Theorem 4 involves limits of these majorants at infinity. We also obtain a nonoscillation criterion involving similar limits.

Mathematical Subject Classification

Primary: 35.11

Milestones

Received: 25 January 1968

Published: 1 December 1968