Article
Full entry |
PDF
(0.2 MB)
Feedback
Keywords:
nonoscillatory and oscillatory solution; second order Riccati equation
nonoscillatory and oscillatory solution; second order Riccati equation
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 $Chanturiya$.
References:
[1] Barrett, J. H.: Oscillation Theory of Ordinary Linear Differential Equation. Advances in Math. 3 (1969), 415–509. MR 0257462
[2] Chanturiya, T. A. and Kiguradze, I. T.: Asymptotic properties of solutions of nonautonomous ordinary differential equations. Nauka, Moscow, 1990. (in Russian)
[3] Džurina, J.: Asymptotic properties of third-order differential equations with deviating argument. Czech. Math. J. 44 (1994), 163–172. MR 1257942
[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
[5] Greguš, M.: Linear differential equation of the third order. Veda, Bratislava, 1981. (in Slovak) MR 0657356
[6] Hanan, M.: Oscillation criteria for a third order linear differential equations. Pacific J. Math. 11 (1961), 919–944. MR 0145160
[7] Heidel, J.W.: Qualitative behavior of solutions of a third order nonlinear differential equation. Pacific J. Math. 27 (1968), 507–526. MR 0240389 | Zbl 0172.11703
[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
[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) MR 0173060 | Zbl 0135.14302
[10] Kiguradze, I. T.: Some singular value problems for ordinary differential equations. University Press, Tbilisi (1975). (in Russian) MR 0499402
[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. MR 0193332 | Zbl 0143.31501
[12] Rovder, J.: Oscillation criteria for third-order linear differential equations. Mat. Časopis 25 (1975), 231–244. MR 0412521 | Zbl 0309.34028
[13] Škerlík, A.: Integral criteria of oscillation for a third order linear differential equation. Math. Slovaca (to appear). MR 1387057
[14] Škerlík, A.: Oscillation theorems for third order nonlinear differential equations. Math. Slovaca 42 (1992), 471–484. MR 1195041
[15] Šoltés, V.: Oscillatory properties of solutions of a third order nonlinear differential equations. Math.Slovaca 26 (1976), 217–227. (in Russian)
[16] Swanson, C.A.: Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York-London, 1968. MR 0463570 | Zbl 0191.09904
Search
Partner of