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Results in Mathematics

, Volume 43, Issue 1–2, pp 129–149 | Cite as

Nonoscillation theory for second order half-linear differential equations in the framework of regular variation

  • Jaroslav Jaroš
  • Kusano Takaŝi
  • Tomoyuki Tanigawa
Article

Abstract

Criteria are established for nonoscillation of all solutions of the second order half-linear differential equation
$$(\mid y^\prime \mid^{\alpha-1}y^\prime)^\prime + q(t)\mid y \mid^{\alpha -1}y = 0,\ \ \ t \geq 0,$$
(A)
where α > 0 is a constant and q: [0, ∞) → ℝ is continuous. The criteria are designed to exhibit the role played by the integral of q(t) in guaranteeing the existence of nonoscillatory solutions of (A) in specific classes of regularly varying functions in the sense of Karamata.

2000 Mathematics Subject Classification

34C11 34D05 

Keywords and phrases

nonoscillation slowly varying function regular variation 

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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  • Jaroslav Jaroš
    • 1
  • Kusano Takaŝi
    • 2
  • Tomoyuki Tanigawa
    • 3
  1. 1.Department of Mathematical Analysis, Faculty of Mathematics Physics and InformaticsComenius UniversityBratislavaSlovakia
  2. 2.Department of Applied Mathematics, Faculty of ScienceFukuoka UniversityFukuokaJapan
  3. 3.Department of MathematicsToyama National College of TechnologyToyamaJapan

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