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Zbl 1060.34019
Sun, Yuan Gong; Agarwal, R.P.
Forced oscillation of $n$th-order nonlinear differential equations.
(English)
[J] Funct. Differ. Equ. 11, No. 3-4, 587-596 (2004). ISSN 0793-1786

Summary: We establish some new oscillation criteria for forced nonlinear differential equations of the form $$x^{(n)}(t)+ q(t)|x(t)|^\lambda\text{sgn\,}x(t)= f(t),\qquad\lambda> 1,$$ where the coefficient $q(t)$ is allowed to change its sign and the forcing term $f(t)$ is not required to be the nth derivative of an oscillatory function. We further employ the technique presented here to establish new oscillation criteria for forced nonlinear neutral equations of the form $$\multline (x(t)+ cx[t-\tau])^{(n)}+ a(t) x(t)+ b(t) x[t-\tau]+\\ q(t)|x(t)|^\lambda\text{sgn\,}x(t)+ p(t)|x|[t- \tau]|^\sigma\text{sgn\,}x[t- \tau]= f(t),\endmultline$$ with $\lambda> 1$ and $\sigma> 1$.
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; forced oscillation; neutral equation

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