Previous |  Up |  Next

Article

Keywords:
linear differential equation; quasi-derivative; monotone solution; Kneser solution; oscillatory solution
Summary:
The paper deals with the oscillation of a differential equation $L_4y+P(t)L_2y+Q(t)y\equiv 0$ as well as with the structure of its fundamental system of solutions.
References:
[G] Gera, M.: Nichtoszillatorische und oszillatorische Differentialgleichungen dritter Ordnung. Čas. Pěst. Mat., 96 (1971), 278–293. MR 0291556 | Zbl 0222.34034
[Gr] Greguš, M.: Oszillatorische Eigenschaften der Lösungen der linearen Differentialgleichung dritter Ordnung $y^{\prime \prime \prime } + 2Ay^{\prime } + (A^{\prime } + b)y = 0$, wo $A = A(x) \le 0$ ist. Czechoslovak Math. J., 9(84) (1959), 416–428. MR 0111888
[H] Heidel, J. W.: Qualitative behavior of solutions of a third order nonlinear differential equation. Pac. J. Math., 27 (1968), 507–526. DOI 10.2140/pjm.1968.27.507 | MR 0240389 | Zbl 0172.11703
[LN] Leighton, W. and Nehari, Z.: On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Trans. Amer. Math. Soc., 89 (1958), 325–377. DOI 10.1090/S0002-9947-1958-0102639-X | MR 0102639
[R] Regenda, J.: Oscillation criteria for fourth-order linear differential equations. Math. Slovaca, 29 (1979), 3–16. MR 0561771 | Zbl 0408.34032
[Ro] Rovder, J.: Oscillation criteria for third-order linear differential equations. Mat. Čas., 25 (1975), 231–244. MR 0412521 | Zbl 0309.34028
[S] Shair, A.: On the oscillation of solutions of a class of linear fourth order differential equations. Pac. J. Math., 34 (1970), 289–299. DOI 10.2140/pjm.1970.34.289 | MR 0268455
[Š] Šoltés, V.: Oscillatory properties of solutions of a fourth-order nonlinear differential equation. Math. Slovaca, 29 (1979), 73–82. MR 0561780
[Šv] Švec, M.: Einige asymptotische und oszillatorische Eigenschaften der Differentialgleichung $y^{\prime \prime \prime } + A(x)y^{\prime } + B(x)y = 0$. Czechoslovak Math. J., 15 (1965), 378–393. MR 0185187 | Zbl 0143.11202
[TP] Tóthová, M. and Palumbíny, O.: On monotone solutions of the fourth order ordinary differential equations. Czechoslovak Math. J., 45(120) (1995), 737–746. MR 1354930
Partner of
EuDML logo