New results on the sign of the Green function of a two-point n-th order linear boundary value problem

• Published in: Boundary value problems Vol. 2022; no. 1; pp. 1 - 22
• Main Authors: Almenar, Pedro, Jódar, Lucas
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 26.07.2022; Hindawi Limited; SpringerOpen
• Subjects: Analysis; Approximations and Expansions; Boundary conditions; Boundary value problems; Derivatives; Difference and Functional Equations; Eigenvalues; Green function; Green's functions; Hyperdisfocality; Mathematics; Mathematics and Statistics; n-th order linear differential equation; Ordinary Differential Equations; Partial Differential Equations; Signs; Two-point boundary value problem; Two-point boundary value problem; Hyperdisfocality; Green function; th order linear differential equation
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-022-01631-z

This paper provides conditions for determining the sign of all the partial derivatives of the Green functions of n -th order boundary value problems subject to a wide set of homogeneous two-point boundary conditions, removing restrictions of previous results about the distance between the two extremes that define the problem. To do so, it analyzes the sign of the derivatives of the solutions of related two-point n -th order boundary value problems subject to n − 1 boundary conditions by introducing a new property denoted by ‘hyperdisfocality’.