## Forced oscillation of higher-order nonlinear differential equations.(English)Zbl 1099.34034

Here, the forced nonlinear differential equation is considered
$L_nx(t)-q(t)F(x(t)=e(t)),\tag{1}$
where
$L_0x(t)=x(t);\quad L_\kappa x(t)=a_\kappa(t)(L_{\kappa-1}x(t))',\quad\kappa=1,2,\dots,n,\;'=\tfrac{d}{dt},$
$$a_i$$, $$q:[t_0,\infty]\to(0,\infty)$$, $$i=1,2,\dots,n-1$$, $$a_n\equiv1$$, $$e:[t_0,\infty)\to\mathbb{R}$$, $$F:\mathbb{R}\to\mathbb{R}$$ are continuous and $$x F([x])>0$$ for $$x\neq 0$$.
Some new criteria are established for the oscillation of higher-order forced nonlinear differential equations of the form (1), according to a smart choice of a class of new auxiliary functions. The main results of this paper are different from most known ones in the sense that they are given in the form $$\liminf_{t\to\infty}[\cdot]<0$$.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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### References:

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