Vol. 17, No. 3, 1966

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The behavior of solutions of the differential equation y′′′ + p(x)y + q(x)y = 0

Alan Cecil Lazer

Vol. 17 (1966), No. 3, 435–466

This paper is a study of the oscillation and other properties of solutions of the differential equation

y′′′ + p(x)y′ +q(x)y = 0.

Throughout, we shall assume that p(x) and q(x) are continuous and do not change sign on the infinite half-axis I : a x < +. A solution of (L) will be said to be oscillatory if it change sign for arbitrarily large values of x.

Our principal results will be concerned with the existence, uniqueness, (aside from constant multiples) and asymptotic behavior of nontrivial, nonoscillatory solutions, and criteria for the existence of oscillatory solutions in terms of the behavior of nonoscillatory solutions. Other results are concerned with separation properties and the question of when the amplitudes of oscillatory solutions are increasing or decreasing.

Mathematical Subject Classification
Primary: 34.42
Received: 2 June 1964
Published: 1 June 1966
Alan Cecil Lazer