Forced oscillation of \(n\)th-order nonlinear differential equations. (English) Zbl 0958.34050

The authors state new oscillation criteria for forced nonlinear equations \[ (x^{(n)}(t)-q(t)|x(t)|^\lambda \text{ sgn}x(t)=f(t),\quad \lambda>1, \tag{*} \] with \(n\geq 1\), the functions \(f,q\) are continuous on \((t_0,\infty)\) and \(q(t)>0\) for \(t\geq t_0\). Examples illustrate that the forcing term \(f\) is not required to be small. There are also established new oscillation criteria for forced nonlinear neutral equations.


34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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