Conditional oscillation of half-linear differential equations with periodic coefficients. (English) Zbl 1212.34110

Hasil, Petr

Arch. Math., Brno 44, No. 2, 119-131 (2008).

Summary: We show that the half-linear differential equation \[ \big [r(t)\Phi (x')\big ]' + \frac {s(t)}{t^p} \Phi (x) = 0 \] with \(\alpha \)-periodic positive functions \(r, s\) is conditionally oscillatory, i.e., there exists a constant \(K>0\) such that the equation with \(\gamma s(t)/t^p\) instead of \(s(t)/t^p\) is oscillatory for \(\gamma > K\) and nonoscillatory for \(\gamma < K\).

MSC:

34C10

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

Keywords:

oscillation theory; conditional oscillation; half-linear differential equation