Vol. 72, No. 2, 1977

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New partial asymptotic stability results for nonlinear ordinary differential equations

Frederick J. Scott

Vol. 72 (1977), No. 2, 523–535

The problem of determining sufficient conditions which that assure that all solutions of the second order equation x′′ + q(t)x = 0 approach zero as t tends to infinity has been studied extensively since 1933. Several results have been given for generalizations of the basic linear equation. In this paper a new technique is used to obtain further results for the equation

(p(t)x ′)′ + q(t)f(x) = e(t).

The generality of the theorems developed is established by showing that a substantial number of previously known results are immediate consequences of the work herein. Of particular interest is the fact that three recent theorems by Burton and Grimmer, which appeared in this journal, follow from the work contained in this paper.

Mathematical Subject Classification 2000
Primary: 34D05
Received: 25 June 1976
Published: 1 October 1977
Frederick J. Scott