RT Journal Article
T1 Characterization of the spectra of the Hill's equation coupled to different boundary value conditions and application to nonlinear boundary problems
A1 Cabada Fernández, Alberto
A1 López Somoza, Lucía
A1 Yousfi Khoumsi, Mouhcine
K1 Hill's Equation
K1 Green's Function
AB In this paper we will characterize the spectrum of the second order Hill’s equation coupled to several boundary value conditions. More concisely, the idea consists of study the spectrum of the second-order differential Hill’s equation coupled to Initial, Final, Neumann, Dirichlet, Periodic and Mixed boundary conditions, by applying the equality (10) proved by the authors in [5] and expressing the Green’s function of the Hill’s equation coupled to a given boundary condition as a combination of the Green’s function related to another different boundary condition. These spectra are characterized as suitable sets of real values that verify an equality that depends on the Green’s function of each case. We will also deduce some properties of these spectra and identities between Green’s functions. The work continuous on the lines initiated on [6] and [3]. It is important to remark that the ideas and arguments used to deduce the comparison between the corresponding spectrum of the considered problems, and their characterization in many cases, are completely different to the ones used in [3].
PB Faculty of Sciences and Mathematics, Department of Mathematics, Serbia
SN 0354-5180
YR 2024
FD 2024
LK https://hdl.handle.net/10347/39740
UL https://hdl.handle.net/10347/39740
LA eng
NO The first and the second authors are supported by Grant PID2020-113275GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” of the “European Union”.
DS Minerva
RD 22 abr 2026