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

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

Zbl 0078.07602