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

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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.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mathematics Physics and Informatics, Comenius University, 842 15, Bratislava, Slovakia

    Jaroslav Jaroš

  2. Department of Applied Mathematics, Faculty of Science, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka, 814-0180, Japan

    Kusano Takaŝi

  3. Department of Mathematics, Toyama National College of Technology, 13 Hongo-cho, Toyama, 939-8630, Japan

    Tomoyuki Tanigawa

Authors
  1. Jaroslav Jaroš
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  2. Kusano Takaŝi
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  3. Tomoyuki Tanigawa
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Correspondence to Jaroslav Jaroš.

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Jaroš, J., Takaŝi, K. & Tanigawa, T. Nonoscillation theory for second order half-linear differential equations in the framework of regular variation. Results. Math. 43, 129–149 (2003). https://doi.org/10.1007/BF03322729

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