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Convergent Disfocality and Nondisfocality Criteria for Second‐Order Linear Differential Equations

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  • Pedro Almenar
  • Lucas Jódar

Abstract

This paper presents a method to determine whether the second‐order linear differential equation y′′ + q(x)y = 0 is either disfocal or nondisfocal in a fixed interval. The method is based on the recursive application of a linear operator to certain functions and yields upper and lower bounds for the distances between a zero and its adjacent critical points, which will be shown to converge to the exact values of such distances as the recursivity index grows.

Suggested Citation

  • Pedro Almenar & Lucas Jódar, 2013. "Convergent Disfocality and Nondisfocality Criteria for Second‐Order Linear Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:987976
    DOI: 10.1155/2013/987976
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    References listed on IDEAS

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    1. Pedro Almenar & Lucas Jódar, 2013. "The Distribution of Zeroes and Critical Points of Solutions of a Second Order Half‐Linear Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Pedro Almenar & Lucas Jódar, 2013. "The Distribution of Zeroes and Critical Points of Solutions of a Second Order Half-Linear Differential Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, May.
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    1. Pedro Almenar & Lucas Jódar, 2014. "The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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