Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality

In this paper, the authors present new oscillation criteria for the noncanonical second-order delay differential equation with mixed nonlinearities (a(t)x′(t))′+∑j=1nqj(t)xαj(σj(t))=0using an arithmetic–geometric mean inequality. We establish our results first by transforming the studied equation in...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-11, Vol.23 (S1), Article 269
Main Authors: Purushothaman, Ganesh, Suresh, Kannan, Thandapani, Ethiraju, Tunç, Ercan
Format: Article
Language:English
Subjects:
Arithmetic
Canonical forms
Criteria
Differential equations
Inequalities
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Summary:In this paper, the authors present new oscillation criteria for the noncanonical second-order delay differential equation with mixed nonlinearities (a(t)x′(t))′+∑j=1nqj(t)xαj(σj(t))=0using an arithmetic–geometric mean inequality. We establish our results first by transforming the studied equation into canonical form and then applying a comparison technique and integral averaging method to get new oscillation criteria. Examples are provided to illustrate the importance and novelty of their main results.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01130-9