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

Grammatikopoulos, Myron K., and Marušiak, Pavol. "Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients." Archivum Mathematicum 031.1 (1995): 29-36. <http://eudml.org/doc/247690>.

@article{Grammatikopoulos1995,
abstract = {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 $\ \liminf \limits _\{t\rightarrow \infty \}|x(t)|=0.$},
author = {Grammatikopoulos, Myron K., Marušiak, Pavol},
journal = {Archivum Mathematicum},
keywords = {neutral differential equations; oscillatory (nonoscillatory) solutions; second-order differential inequalities; oscillatory},
language = {eng},
number = {1},
pages = {29-36},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients},
url = {http://eudml.org/doc/247690},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Grammatikopoulos, Myron K.
AU - Marušiak, Pavol
TI - Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 1
SP - 29
EP - 36
AB - 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 $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$
LA - eng
KW - neutral differential equations; oscillatory (nonoscillatory) solutions; second-order differential inequalities; oscillatory
UR - http://eudml.org/doc/247690
ER -