Oscillation properties of certain self-adjoint differential equations of the fourth order

Gary Douglas Jones and Samuel Murray Rankin, III

Vol. 63 (1976), No. 1, 179–184

DOI: 10.2140/pjm.1976.63.179

Abstract

Assuming oscillation, a connection between the decreasing and increasing solutions of

(1)

is established. With this result, it is shown that if r ≡ 1 and p positive and monotone the decreasing solution of (1) is essentially unique. It is also shown that if p > 0 and r ≡ 1 the decreasing solution tends to zero.

Mathematical Subject Classification 2000

Primary: 34C10

Milestones

Received: 13 November 1975

Published: 1 March 1976