On the Zeroes and the Critical Points of a Solution of a Second Order Half‐Linear Differential Equation

Pedro Almenar and Lucas Jódar

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second‐order half‐linear differential equation (p(x)Φ(y′))′ + q(x)Φ(y) = 0, with p(x) and q(x) piecewise continuous and p(x) > 0, Φ(t) = |t|r−2t and r being real such that r > 1. It also compares between them in several examples. Lower bounds (i.e., Lyapunov inequalities) for such a distance are also provided and compared with other methods.

Date: 2012
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https://doi.org/10.1155/2012/787920

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:787920

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