Criteria and estimates for decaying oscillatory solutions for some second-order quasilinear ODEs

Date

2017-01-24

Authors

T, Tadie

Journal Title

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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.

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Attribution 4.0 International

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