zbMATH — the first resource for mathematics

Oscillation criteria for differential equation \(y^{(4)}+P(t)y''+R(t)y'+Q(t)y=0\). (English) Zbl 0598.34028
This paper is concerned with the oscillation of the differential equation \[ (R)\quad y^{(4)}+P(t)y''+R(t)y'+Q(t)y=0, \] where P(t), R(t), Q(t) are real-valued continuous functions on the interval \(I=<a,\infty)\), \(- \infty <a<\infty\). We assume throughout that (B) P(t)\(\leq 0\), R(t)\(\leq 0\), \(R^ 2(t)\leq 2P(t)Q(t)\) or (C) P(t)\(\leq R(t)\leq 0\), 2Q(t)\(\leq R(t)\) for all \(t\in I\) and Q(t) not identically zero in any subinterval of I. One can verify easily that (C) implies (B). Oscillation theorems and criteria for equation (R) are proved.

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
Full Text: EuDML
[1] AHMAD SHAIR: On the oscillation of solutions of a class of linear fourth order differential equations. Pac. J. Math. 34, 1970. · Zbl 0176.20402
[2] LEIGHTON W., NEHARI Z.: On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. Trans. Amer. Math. Soc., 89, 1958. · Zbl 0084.08104
[3] REGENDA J.: Oscillation and nonoscillation properties of the solutions of the differential equation y(4)+P(t)y” + Q(t)y = 0. Math. Slov., 28, 1978. · Zbl 0406.34041
[4] REGENDA J.: Oscillation criteria for fourth order linear differential equations. Math. Slov., 29, 1979. · Zbl 0408.34032
[5] REGENDA J.: On the oscillation of solutions of a class of linear fourth order differential equations. Czech. Math. J., 33 (108) 1983, Praha. · Zbl 0547.34023
[6] REGENDA J.: Oscillation theorems for a class of linear fourth order differential equations. Czech Math. J.) · Zbl 0542.34030
[7] GREGUŠ M.: Third-order linear differential equation. (Slovak), Veda, Bratislava 1981. · Zbl 0486.34047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.