Vol. 28, No. 1, 1969

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Nonoscillatory solutions of second order nonlinear differential equations

Lynn Harry Erbe

Vol. 28 (1969), No. 1, 77–85
Abstract

We consider here a generalization of the equation

x′′ + a(t)x2n+1 = 0

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
Authors
Lynn Harry Erbe