An oscillation theorem for second order superlinear differential equations
The differential equation under consideration is (1) \(-y'' =p |y |^a \text{sgn} y\) in \(\mathbb{R}_+\), where \(a>1\) is a constant and \(p\in C (\mathbb{R}_+, \mathbb{R})\). Sufficient conditions on \(p\) are given for equation (1) to be oscillatory at \(\infty\). A historical review describes earlier results of the same type by \textit{A. Wintner} [Q. Appl. Math. 7, 115-117 (1949; Zbl 0032.34801)], \textit{Ph. Hartman} [Am. J. Math. 74, 389-400 (1952; Zbl 0048.06602)], \textit{I. V. Kamenev} [Mat. Zametki 10, 129-134 (1971; Zbl 0237.34057)], \textit{G. J. Butler} [SIAM J. Math. Anal. 11, 190-200 (1980; Zbl 0424.34033)], and \textit{J. S. W. Wong} [Proc. Am. Math. Soc. 106, 1069-1077 (1989; Zbl 0694.34027)].
scientific article; zbMATH DE number 941301