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

• Ganesh Purushothaman ^[2] ; Kannan Suresh ^[2] ; Ethiraju Thandapani ^[1] ; Ercan Tunç ^[3]
  1. [1] University of Madras

     University of Madras

     India

     
  2. [2] St. Joseph’s College of Engineering
  3. [3] Tokat Gaziosmanpa¸sa University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
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  • In this paper, the authors present new oscillation criteria for the noncanonical secondorder delay differential equation with mixed nonlinearities (a(t)x (t)) + n j=1 q j (t)xαj (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.