Forced oscillation of \(n\)th-order nonlinear differential equations
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.
scientific article; zbMATH DE number 1528561
scientific article