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The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions

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  • Pedro Almenar
  • Lucas Jódar

Abstract

This paper presents a method to obtain lower and upper bounds for the minimum distance between points a and b of the solution of the second order linear differential equation y′′ + q(x)y = 0 satisfying general separated boundary conditions of the type a11y(a) + a12y′(a) = 0 and a21y(b) + a22y′(b) = 0. The method is based on the recursive application of a linear operator to certain functions, a recursive application that makes these bounds converge to the exact distance between a and b as the recursivity index grows. The method covers conjugacy and disfocality as particular cases.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:126713
    DOI: 10.1155/2014/126713
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    References listed on IDEAS

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    1. Pedro Almenar & Lucas Jódar, 2013. "Convergent Disfocality and Nondisfocality Criteria for Second-Order Linear Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, December.
    2. 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).
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