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Some Oscillation Theorems for Second Order Differential Equations

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Abstract

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation

$$(r(t)\Phi (u'(t)))' + c(t)\Phi (u(t)) = 0,$$

where

(i) r,c ∈ C([t 0, ∞), ℝ := (− ∞, ∞)) and r(t) > 0 on [t 0, ∞) for some t 0 ⩾ 0;

(ii) Φ(u) = |u|p−2 u for some fixed number p > 1.

We also generalize some results of Hille-Wintner, Leighton and Willet.

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Authors and Affiliations

  1. National United University, No. 1, Lein Kung, Kung Chin Li, Miaoli City, Taiwan, Republic of China

    Chung-Fen Lee

  2. Department of Information Management, Long-Hua University of Science and Technology, Kei-San, Taoyuan, 333, Taiwan, Republic of China

    Cheh-Chih Yeh

  3. National Jui-Fang Industrial and Vocational Senior High School, No. 60, Jui-Fang-St, Jui-Fang Town, Taipei Country, Taiwan, Republic of China

    Chuen-Yu Gau

Authors
  1. Chung-Fen Lee
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  2. Cheh-Chih Yeh
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  3. Chuen-Yu Gau
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Lee, CF., Yeh, CC. & Gau, CY. Some Oscillation Theorems for Second Order Differential Equations. Czech Math J 55, 845–861 (2005). https://doi.org/10.1007/s10587-005-0070-5

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  • DOI: https://doi.org/10.1007/s10587-005-0070-5

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