Oscillation criteria for certain nonlinear differential equations
The author studies the second-order ordinary differential equation \[ x''(t)+p(t)f(x(t))g(x'(t))=0,\tag{1} \] and the delay differential equations \[ x''(t)+p(t)f(x(\tau (t)))g(x'(t))=0\tag{2} \] and \[ x''(t)+p(t)f(x(t),x(\tau (t)))g(x'(t))=0 \tag{3} \] for \(t\geq t_0\). He obtains oscillation criteria for equations (1), (2) and (3), complements those given by \textit{S. R. Grace} and \textit{B. S. Lalli} [J. Math. Anal. Appl. 123, 584-588 (1987; Zbl 0641.34031)] and \textit{G.G. Hamedani and G.S. Krenz} [J. Math. Anal. Appl. 149, No. 1, 271-276 (1990; Zbl 0701.34043)] and handles the cases which are not covered by known criteria. The results are obtained by using an integral averaging technique.
scientific article; zbMATH DE number 1251422
scientific article