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

Pedro Almenar and Lucas Jódar

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/126713

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:126713

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