RT Journal Article
T1 Relationship of Green's functions related to Hill's equation coupled to different boundary conditions
A1 Cabada Fernández, Alberto
A1 López Somoza, Lucía
A1 Yousfi, Mouhcine
K1 Green's function
K1 Hill's equation
K1 Comparison results
K1 Nonlinear boundary value problems
AB In this paper, we deduce several properties of Green's functions related to Hill's equation coupled to various boundary value conditions. In particular, the idea is to study Green's functions of the second order differential operator coupled to the Neumann, Dirichlet, periodic and mixed boundary conditions, by expressing Green's function of a given problem as a linear combination of Green's functions of the other problems. This will allow us to compare different Green's functions when their sign is constant. Finally, such properties of Green's function of the linear problem will be fundamental to deduce the existence of solutions to the nonlinear problem. The results are derived from the fixed point theory applied to the related operators defined on suitable cones in Banach spaces.
PB Georgian National Academy of Sciences and the A. Razmadze Mathematical Institute
SN 1512-0015
YR 2025
FD 2025-03-31
LK https://hdl.handle.net/10347/42656
UL https://hdl.handle.net/10347/42656
LA eng
NO Mem. Differ. Equ. Math. Phys. 94 (2025), 13–43.
NO The research was supported by Xunta de Galicia (Spain), project # EM2014/032 and 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