On second order quasilinear oscillations. (English) Zbl 1140.34356

Wang, Jingfa

Funkc. Ekvacioj, Ser. Int. 41, No. 1, 25-54 (1998).

From the introduction: This paper is concerned with the oscillatory (and nonoscillatory) behavior of solutions of second order quasilinear differential equations of the type \[ (|y'|^{\alpha-1}y')'+f(t,y)=0, t\geq 0, \] where \(\alpha>0\) is a constant, \(f: [0,\infty)\times\mathbb{R}\to\mathbb{R}\) is a continuous function, and \(\text{sgn}f(t,y)=\text{sgn} y\) for each \(t\in[0,\infty)\). Our purpose is to develop an oscillation theory for such a general case.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations