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

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 = 1 n q j ( t ) x α j ( σ j ( t ) ) = 0 using an arithmetic–geometric mean inequality. We establish our results first by t...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024, Vol.23 (Suppl 1)
Main Authors: Purushothaman, Ganesh, Suresh, Kannan, Thandapani, Ethiraju, Tunç, Ercan
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Online Access:Get full text
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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 = 1 n q j ( t ) x α j ( σ j ( t ) ) = 0 using 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