T, Tadie2022-03-212022-03-212017-01-24Tadie (2017). Criteria and estimates for decaying oscillatory solutions for some second-order quasilinear ODEs. <i>Electronic Journal of Differential Equations, 2017</i>(28), pp. 1-10.1072-6691https://hdl.handle.net/10877/15533Oscillation criteria for the solutions of quasilinear second order ODE are revisited. In our early works [6, 7], we obtained basic oscillation criteria for {φα (u′(t))|′ + αc(t)φβ (u(t)) = 0 by estimating of the diameters of the nodal set of the solutions. The focus of this work is to estimate the decay of the oscillatory solutions. Let u be a strongly oscillatory solution, (tm) the increasing sequence of zeros of u′, and Dm the nodal set of u that contains tm. We estimate |u(tm)|∞ ≔ max t∈Dm |u(t)| and the diameter of Dm as m → ∞.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalOscillation criteria for ODEEstimates of decaying solutionsArticle