Improving Results on Solvability of a Class of th-Order Linear Boundary Value ProblemsReport as inadecuate

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International Journal of Differential Equations - Volume 2016 2016, Article ID 3750530, 10 pages -

Research Article

Vodafone Spain, Avenida América 115, 28042 Madrid, Spain

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s-n, 46022 Valencia, Spain

Received 11 April 2016; Revised 9 June 2016; Accepted 19 June 2016

Academic Editor: Elena Braverman

Copyright © 2016 Pedro Almenar and Lucas Jódar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a modification of a recursive method described in a previous paper of the authors, which yields necessary and sufficient conditions for the existence of solutions of a class of th-order linear boundary value problems, in the form of integral inequalities. Such a modification simplifies the assessment of the conditions on restricting the inequality to be verified to a single point instead of the full interval where the boundary value problem is defined. The paper also provides an error bound that needs to be considered in the integral inequalities of the previous paper when they are calculated numerically.

Author: Pedro Almenar and Lucas Jódar



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