Oscillation Criteria for Certain Nonlinear Differential Equations
Copyright policy )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.
Averaging method for ordinary differential equations, Delay, 2Nd-Order, Applied Mathematics, Nonlinear oscillations and coupled oscillators for ordinary differential equations, averaging method, nonlinear oscillations, oscillation theory, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Analysis
Averaging method for ordinary differential equations, Delay, 2Nd-Order, Applied Mathematics, Nonlinear oscillations and coupled oscillators for ordinary differential equations, averaging method, nonlinear oscillations, oscillation theory, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Analysis
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