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On Constants in Nonoscillation Criteria for Half‐Linear Differential Equations

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  • Simona Fišnarová
  • Robert Mařík

Abstract

We study the half‐linear differential equation (r(t)Φ(x′)) ′ + c(t)Φ(x) = 0, where Φ(x) = |x|p−2x, p > 1. Using the modified Riccati technique, we derive new nonoscillation criteria for this equation. The results are closely related to the classical Hille‐Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a certain one‐parametric expression.

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Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:638271
DOI: 10.1155/2011/638271
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