RT Journal Article
T1 Spectral characterization of the constant sign derivatives of Green’s function related to two point boundary value conditions
A1 Cabada Fernández, Alberto
A1 López Somoza, Lucía
A1 Yousfi Khoumsi, Mouhcine
K1 Green’s function
K1 Two-point boundary conditions
K1 Spectral theory
K1 Comparison results
K1 Constant sign
AB In this paper we will consider a n-th order linear operator Tn[M], depending on a real parameter M, coupled to different two-point boundary conditions, and we will study the set of parameters for which certain partial derivatives of the related Green’s function are of constant sign. We will do it without using the explicit expression of the Green’s function. In particular, the set of parameters for which the derivatives of the Green’s function have constant sign will be an interval whose extremes are characterized as the first eigenvalues of the studied operator related to suitable boundary conditions. As a consequence of the main result, we will be able to give sufficient conditions to ensure that the derivatives of the Green’s function cannot be nonpositive (nonnegative). These characterizations and the obtained results can be used to deduce the existence of solutions of nonlinear problems under additional conditions on the nonlinear part. In order to illustrate the obtained results, some examples are given.
PB Birkhäuser
SN 1575-5460
YR 2024
FD 2024-12-12
LK https://hdl.handle.net/10347/39830
UL https://hdl.handle.net/10347/39830
LA eng
NO Cabada, A., López-Somoza, L. & Yousfi, M. Spectral Characterization of the Constant Sign Derivatives of Green’s Function Related to Two Point Boundary Value Conditions. Qual. Theory Dyn. Syst. 24, 38 (2025). https://doi.org/10.1007/s12346-024-01193-8
NO This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s12346-024-01193-8
NO The three authors were partially supported by Grant PID2020-113275GB-I00, funded by MCIN/AEI/10.13039/501100011033 and by “ERDFAway of making Europe” of the “European Union”, and by Xunta de Galicia (Spain), project ED431C 2023/12.
DS Minerva
RD 28 abr 2026