Strong oscillation and nonoscillation of quasilinear differential equations of second order. (English) Zbl 0869.34031

Takaŝi, Kusano; Naito, Yūki; Ogata, Akio

Differ. Equ. Dyn. Syst. 2, No. 1, 1-10 (1994).

Summary: It is shown that Nehari’s well-known criteria [Z. Nehari, Trans. Am. Math. Soc. 85, 428-445 (1957; Zbl 0078.07602)] for strong oscillation and nonoscillation of the linear differential equation \(y''+\lambda q(t)y=0\) can naturally be extended to a class of nonlinear differential equations of the form \((|y'|^\alpha\text{sgn }y')'+\lambda q(t)|y|^\alpha\text{sgn }y=0\), \(\alpha>0\).

MSC:

34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Keywords:

Nehari’s criteria; strong oscillation; nonoscillation

Citations:

Zbl 0078.07602