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Keywords:
neutral differential equations; oscillatory (nonoscillatory) solutions
neutral differential equations; oscillatory (nonoscillatory) solutions
Summary:
This paper deals with the second order nonlinear neutral differential inequalities $(A_\nu )$: $(-1)^\nu x(t)\,\lbrace \,z^{\prime \prime }(t)+(-1)^\nu q(t)\,f(x(h(t))) \rbrace \le 0,\ $ $t\ge t_0\ge 0,$ where $\ \nu =0\ $ or $\ \nu =1,\ $ $\ z(t)\,=\,x(t)\,+\,p(t)\,x(t-\tau ),\ $ $\ 0<\tau =\ $ const, $\ p,q,h:[t_0,\infty )\rightarrow R\ $ $\ f:R\rightarrow R\ $ are continuous functions. There are proved sufficient conditions under which every bounded solution of $(A_\nu )$ is either oscillatory or $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$
References:
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