Geodesic
Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients
Archivum mathematicum, Tome 31 (1995) no. 1, pp. 29-36 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$
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 $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$
Classification : 34A40, 34C10, 34K11, 34K15, 34K25, 34K40
Keywords: neutral differential equations; oscillatory (nonoscillatory) solutions 
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     author = {Grammatikopoulos, M. K. and Maru\v{s}iak, P.},
     title = {Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1995_31_1_a2/}
}
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Grammatikopoulos, M. K.; Marušiak, P. Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients. Archivum mathematicum, Tome 31 (1995) no. 1, pp. 29-36. http://geodesic.mathdoc.fr/item/ARM_1995_31_1_a2/

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