## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2015 (2015), Article ID 230405, 19 pages.

### Solvability of *N*th Order Linear Boundary Value Problems

P. Almenar and L. Jódar

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#### Abstract

This paper presents a method that provides necessary and sufficient conditions for the existence of solutions of *n*th order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2015 (2015), Article ID 230405, 19 pages.

**Dates**

Received: 27 July 2015

Accepted: 4 October 2015

First available in Project Euclid: 20 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1484881447

**Digital Object Identifier**

doi:10.1155/2015/230405

**Mathematical Reviews number (MathSciNet)**

MR3421160

**Zentralblatt MATH identifier**

1339.34034

#### Citation

Almenar, P.; Jódar, L. Solvability of N th Order Linear Boundary Value Problems. Int. J. Differ. Equ. 2015 (2015), Article ID 230405, 19 pages. doi:10.1155/2015/230405. https://projecteuclid.org/euclid.ijde/1484881447

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