Criteria and estimates for decaying oscillatory solutions for some second-order quasilinear ODEs
Date
2017-01-24
Authors
T, Tadie
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Oscillation 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 → ∞.
Description
Keywords
Oscillation criteria for ODE, Estimates of decaying solutions
Citation
Tadie (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.
Rights
Attribution 4.0 International