| Title:
|
Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives (English) |
| Author:
|
Bartušek, Miroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
245-259 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions are given under which the sequence of the absolute values of all local extremes of $y^{[i]}$, $i\in \lbrace 0,1,\dots , n-2\rbrace $ of solutions of a differential equation with quasiderivatives $y^{[n]}=f(t,y^{[0]},\dots , y^{[n-1]})$ is increasing and tends to $\infty $. The existence of proper, oscillatory and unbounded solutions is proved. (English) |
| MSC:
|
34C10 |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 0930.34023 |
| idMR:
|
MR1452419 |
| . |
| Date available:
|
2009-09-24T10:04:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127355 |
| . |
| Reference:
|
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| Reference:
|
[2] M. Bartušek: The asymptotic behaviour of solutions of the differential equation of the third order.Arch. Math. XX (1984), no. 3, 101–112. MR 0784861 |
| Reference:
|
[3] M. Bartušek: The asymptotic behaviour of oscillatory solutions of the equation of the fourth Order.Arch. Math. 21 (1985), no. 2, 93–104. MR 0817551 |
| Reference:
|
[4] M. Bartušek: On oscillatory solution of the differential equation of the $n$-th order.Arch. Math. 22 (1986), no. 3, 145–156. MR 0868130 |
| Reference:
|
[5] M. Bartušek: Asymptotic Properties of Oscillatory Solutions of Differential Equations of the $n$-th Order.FOLIA FSN Univ. Masaryk. Brunensis, Math. 3, Masaryk Univ. Brno, 1992. MR 1271586 |
| Reference:
|
[6] M. Bartušek: Oscillatory criteria for nonlinear $n$-th order differential equations with quasi-derivatives.Georgian Math. J. 3 (1996), no. 4, 301–314. MR 1397813, 10.1007/BF02256721 |
| Reference:
|
[7] Š. Belohorec: Monotone and oscillatory solutions of a class of nonlinear differential equations.Math. Čas. 19 (1969), no. 3, 169–187. Zbl 0271.34045, MR 0304773 |
| Reference:
|
[8] I. Bihari: Oscillation and monotonicity theorems concerning non-linear differential equations of the second order.Acta Math. Acad. Sci. Hung. IX (1958), no. 1–2, 83–104. MR 0095321, 10.1007/BF02023866 |
| Reference:
|
[9] D. Bobrowski: Some properties of oscillatory solutions of certain differential equations of second order.Ann. Soc. Math. Polonae XI (1967), 39–48. Zbl 0166.35002, MR 0218668 |
| Reference:
|
[10] K.M. Das: Comparison and monotonicity theorems for second order non-linear differential equations.Acta Math. Acad. Sci. Hung. 15 (1964), no. 3–4, 449–456. MR 0176155, 10.1007/BF01897153 |
| Reference:
|
[11] I. Foltyńska: On certain properties of oscillatory solutions of the second order nonlinear differential equation (Polish).Fasc. Math. 4 (1969), 57–64. |
| Reference:
|
[12] I.T. Kiguradze: Some Singular Boundary-Value Problems for Ordinary Differential Equations.Izd. Tbiliss. Univ., Tbilisi, 1975. (Russian) MR 0499402 |
| Reference:
|
[13] I.T. Kiguradze: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Nauka, Moscow, 1990. (Russian) |
| . |
