| Title:
|
An integral condition of oscillation for equation $y'''+p(t)y'+q(t)y=0$ with nonnegative coefficients (English) |
| Author:
|
Škerlík, Anton |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
155-161 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our aim in this paper is to obtain a new oscillation criterion for equation \[ y^{\prime \prime \prime }+ p(t)y^{\prime } + q(t)y = 0 \] with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation $ y^{\prime \prime \prime }+ q(t)y = 0$, our results solve the open question of $Chanturiya$. (English) |
| Keyword:
|
nonoscillatory and oscillatory solution |
| Keyword:
|
second order Riccati equation |
| MSC:
|
34C10 |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 0843.34039 |
| idMR:
|
MR1357983 |
| . |
| Date available:
|
2008-06-06T21:28:37Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107535 |
| . |
| Reference:
|
[1] Barrett, J. H.: Oscillation Theory of Ordinary Linear Differential Equation.Advances in Math. 3 (1969), 415–509. MR 0257462 |
| Reference:
|
[2] Chanturiya, T. A. and Kiguradze, I. T.: Asymptotic properties of solutions of nonautonomous ordinary differential equations.Nauka, Moscow, 1990. (in Russian) |
| Reference:
|
[3] Džurina, J.: Asymptotic properties of third-order differential equations with deviating argument.Czech. Math. J. 44 (1994), 163–172. MR 1257942 |
| Reference:
|
[4] Erbe, L.: Existence of oscillatory solutions and asymtotic behavior for a class of a third order linear differential equations.Pacific J. Math. 64 (1976), 369–385. MR 0435508 |
| Reference:
|
[5] Greguš, M.: Linear differential equation of the third order.Veda, Bratislava, 1981. (in Slovak) MR 0657356 |
| Reference:
|
[6] Hanan, M.: Oscillation criteria for a third order linear differential equations.Pacific J. Math. 11 (1961), 919–944. MR 0145160 |
| Reference:
|
[7] Heidel, J.W.: Qualitative behavior of solutions of a third order nonlinear differential equation.Pacific J. Math. 27 (1968), 507–526. Zbl 0172.11703, MR 0240389 |
| Reference:
|
[8] Khvedelidze, N. N., Chanturiya, T. A.: Oscillation of solutions of third-order linear ordinary differential equations.Differencialnye Uravneniya 27 (1991), no. 3, 4, 452–460, 611–618. (in Russian) MR 1109137 |
| Reference:
|
[9] Kiguradze, I. T.: On the oscillation of solutions of the equation $d^m/dt^m+a(t)|u|^n sign\,u= 0$.Mat. Sb. 65 (1964), 172–187. (in Russian) Zbl 0135.14302, MR 0173060 |
| Reference:
|
[10] Kiguradze, I. T.: Some singular value problems for ordinary differential equations.University Press, Tbilisi (1975). (in Russian) MR 0499402 |
| Reference:
|
[11] Lazer, A. C.: The behavior of solutions of the differential equation $y^{\prime \prime \prime } + p(x)y^{\prime } + q(x)y = 0$.Pacific J. Math. 17 (1966), 435–466. Zbl 0143.31501, MR 0193332 |
| Reference:
|
[12] Rovder, J.: Oscillation criteria for third-order linear differential equations.Mat. Časopis 25 (1975), 231–244. Zbl 0309.34028, MR 0412521 |
| Reference:
|
[13] Škerlík, A.: Integral criteria of oscillation for a third order linear differential equation.Math. Slovaca (to appear). MR 1387057 |
| Reference:
|
[14] Škerlík, A.: Oscillation theorems for third order nonlinear differential equations.Math. Slovaca 42 (1992), 471–484. MR 1195041 |
| Reference:
|
[15] Šoltés, V.: Oscillatory properties of solutions of a third order nonlinear differential equations.Math.Slovaca 26 (1976), 217–227. (in Russian) |
| Reference:
|
[16] Swanson, C.A.: Comparison and Oscillation Theory of Linear Differential Equations.Academic Press, New York-London, 1968. Zbl 0191.09904, MR 0463570 |
| . |
