Comparison theorems for differential equations of neutral type

Miroslava Růžičková

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 2, page 181-189
  • ISSN: 0862-7959

Abstract

top
We are interested in comparing the oscillatory and asymptotic properties of the equations L n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ f ( t , x ( h ( t ) ) ) = 0 with those of the equations M n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ Q ( t ) q ( x ( r ( t ) ) ) = 0 .

How to cite

top

Růžičková, Miroslava. "Comparison theorems for differential equations of neutral type." Mathematica Bohemica 122.2 (1997): 181-189. <http://eudml.org/doc/248147>.

@article{Růžičková1997,
abstract = {We are interested in comparing the oscillatory and asymptotic properties of the equations $L_n [x(t)-P(t) x(g(t))]+\delta f(t,x(h(t)))=0$ with those of the equations $M_n [x(t)-P(t) x(g(t))]+\delta Q(t)q(x(r(t)))=0.$},
author = {Růžičková, Miroslava},
journal = {Mathematica Bohemica},
keywords = {neutral differential equations; oscillatory solutions; property $\mathcal \{A\}$; property $\mathcal \{B\}$; quasi-derivatives; neutral differential equations; oscillatory solutions; property ; property },
language = {eng},
number = {2},
pages = {181-189},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Comparison theorems for differential equations of neutral type},
url = {http://eudml.org/doc/248147},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Růžičková, Miroslava
TI - Comparison theorems for differential equations of neutral type
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 2
SP - 181
EP - 189
AB - We are interested in comparing the oscillatory and asymptotic properties of the equations $L_n [x(t)-P(t) x(g(t))]+\delta f(t,x(h(t)))=0$ with those of the equations $M_n [x(t)-P(t) x(g(t))]+\delta Q(t)q(x(r(t)))=0.$
LA - eng
KW - neutral differential equations; oscillatory solutions; property $\mathcal {A}$; property $\mathcal {B}$; quasi-derivatives; neutral differential equations; oscillatory solutions; property ; property
UR - http://eudml.org/doc/248147
ER -

References

top
  1. J. Džurina, 10.1002/mana.19931640103, Math. Nachr. 164 (1993), 13-22. (1993) MR1251452DOI10.1002/mana.19931640103
  2. S. R. Grace, B. S. Lalli, 10.1002/mana.19891440106, Math. Nachr. 144 (1989), 65-79. (1989) Zbl0714.34106MR1037161DOI10.1002/mana.19891440106
  3. J. R. Graef, P. W. Spikes, 10.1016/0377-0427(92)90235-P, J. Comput. Appl. Math. 41 (1992). 35-40. (1992) Zbl0757.34058MR1181706DOI10.1016/0377-0427(92)90235-P
  4. M. K. Grammatikopoulos P. Marušiak, Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients, Arch. Math. (Brno) 31 (1995), 29-36. (1995) MR1342372
  5. J. Jaroš, T. Kusano, 10.32917/hmj/1206129616, Hiroshima Math. J. 18 (1988), 509-531. (1988) MR0991245DOI10.32917/hmj/1206129616
  6. G. Ladas, Y. G. Sficas, 10.1017/S0334270000005105, J. Austral. Math. Soc. Ser. B (1986), 502-511. (1986) Zbl0566.34055MR0836222DOI10.1017/S0334270000005105
  7. W. E. Mahfoud, 10.1016/0022-0396(78)90138-9, J. Differential Equations 28 (1978), 437-451. (1978) MR0499605DOI10.1016/0022-0396(78)90138-9
  8. R. Oláh, 10.32917/hmj/1206127821, Hiroshima Math. J. 25 (1995), 1-10. (1995) MR1322598DOI10.32917/hmj/1206127821
  9. M. Růžičková, E. Špániková, On oscillation of functional differential equations of neutral type with the quasi-derivatives, Studies of Univ. of Transp. and Com. 10 (1995), 55-63. (1995) MR1437836
  10. A. Zafer, R. S. Dahiya, 10.1016/0893-9659(93)90010-K, Appl. Math. Lett. 6 (1993), no. 2, 43-46. (1993) Zbl0776.34058MR1347773DOI10.1016/0893-9659(93)90010-K
  11. T. Kusano, M. Naito, 10.2969/jmsj/03330509, J. Math. Soc. Japan 3 (1981), 509-532. (1981) Zbl0494.34049MR0620288DOI10.2969/jmsj/03330509

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.