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### О колеблемости ограниченных решений дифференциальных уравнений с возмущёнными аргументами

Czechoslovak Mathematical Journal

### Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients

Archivum Mathematicum

This paper deals with the second order nonlinear neutral differential inequalities $\left({A}_{\nu }\right)$: ${\left(-1\right)}^{\nu }x\left(t\right)\phantom{\rule{0.166667em}{0ex}}\left\{\phantom{\rule{0.166667em}{0ex}}{z}^{\text{'}\text{'}}\left(t\right)+{\left(-1\right)}^{\nu }q\left(t\right)\phantom{\rule{0.166667em}{0ex}}f\left(x\left(h\left(t\right)\right)\right)\right\}\le 0,\phantom{\rule{4pt}{0ex}}$ $t\ge {t}_{0}\ge 0,$ where $\phantom{\rule{4pt}{0ex}}\nu =0\phantom{\rule{4pt}{0ex}}$ or $\phantom{\rule{4pt}{0ex}}\nu =1,\phantom{\rule{4pt}{0ex}}$ $\phantom{\rule{4pt}{0ex}}z\left(t\right)\phantom{\rule{0.166667em}{0ex}}=\phantom{\rule{0.166667em}{0ex}}x\left(t\right)\phantom{\rule{0.166667em}{0ex}}+\phantom{\rule{0.166667em}{0ex}}p\left(t\right)\phantom{\rule{0.166667em}{0ex}}x\left(t-\tau \right),\phantom{\rule{4pt}{0ex}}$ $\phantom{\rule{4pt}{0ex}}0<\tau =\phantom{\rule{4pt}{0ex}}$ const, $\phantom{\rule{4pt}{0ex}}p,q,h:\left[{t}_{0},\infty \right)\to R\phantom{\rule{4pt}{0ex}}$ $\phantom{\rule{4pt}{0ex}}f:R\to R\phantom{\rule{4pt}{0ex}}$ are continuous functions. There are proved sufficient conditions under which every bounded solution of $\left({A}_{\nu }\right)$ is either oscillatory or $\phantom{\rule{4pt}{0ex}}\underset{t\to \infty }{lim inf}|x\left(t\right)|=0.$

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