On forced oscillation of higher order functional differential equations (Q428118)

The authors consider the \(n\)-th order forced differential equation NEWLINE\[NEWLINEx^{(n)}(t)+q(t)|x(\tau(t))|^{\lambda-1}x(\tau(t))=e(t), \;t\in[t_0,\infty),NEWLINE\]NEWLINE where \(n\geq 1\) is an integer, \(\lambda\) is a constant, \(q, e\in C[t_0,\infty)\), \(\tau\in C^1[t_0,\infty)\), \(\tau'(t)>0\) and \(\lim_{t\to\infty}\tau(t)=\infty\). The following two cases have been taken into consideration: (i) \(q(t)<0, \lambda>1\) and \(\tau(t)\leq t(\geq t)\); (ii) \(q(t)\) changes its sign, \(0<\lambda<1\) and \(\tau(t)\leq t(\geq t)\).