Nonoscillatory solutions of second order nonlinear differential equations

Lynn Harry Erbe

Vol. 28 (1969), No. 1, 77–85

DOI: 10.2140/pjm.1969.28.77

Abstract

We consider here a generalization of the equation

where a(t) is a continuous non-negative function on [0,+∞) and n ≧ 0 is an integer. Necessary and sufficient conditions are given for the existence of

(1) a bounded nonoscillatory solution with prescribed limit at ∞;

(2) a nonoscillatory solution whose derivative has a positive limit at ∞.

Mathematical Subject Classification

Primary: 34.42

Milestones

Received: 19 June 1968

Published: 1 January 1969