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 = 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 inQualitative theory of dynamical systems Vol. 23; no. Suppl 1
Main Authors Purushothaman, Ganesh, Suresh, Kannan, Thandapani, Ethiraju, Tunç, Ercan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2024
Springer Nature B.V
Subjects
Arithmetic
Canonical forms
Criteria
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Inequalities
Mathematics
Mathematics and Statistics
Arithmetic-geometric inequality
34C10
Oscillation
Second-order
Sublinear
Superlinear
34K11
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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