RT Journal Article
T1 Spectral characterization of the constant sign Green’s functions for periodic and Neumann boundary value problems of even order
A1 Cabada Fernández, Alberto
A1 López Somoza, Lucía
K1 Green's function
K1 Periodic boundary conditions
K1 Neumann boundary conditions
K1 Constant sign
K1 Spectral characterization
AB In this paper we will characterize the interval of real parameters M in which the Green’s function GM , related to the operator T2n[M]u(t) := u(2n)(t)+Mu(t) coupled to periodic, u(i)(0) = u(i)(T) , i = 0, . . . ,2n −1, or Neumann, u(2i+1)(0) = u(2i+1)(T) = 0, i =0, . . . ,n−1, boundary conditions, has constant sign on its square of definition. More concisely, we will prove that the optimal values are given as the first zeros of GM(0,0) or GM(T/2,0) , depending both on the sign of GM and on the fact whether 2n is, or is not, a multiple of 4. Such values will be characterized as the eigenvalues of the operator u(2n) related to suitable boundary conditions. This characterization allows us to obtain such values without calculating the exact expression of the Green’s function.
PB Ele-Math
SN 1847-120X
YR 2022
FD 2022-05-01
LK https://hdl.handle.net/10347/38299
UL https://hdl.handle.net/10347/38299
LA eng
DS Minerva
RD 24 abr 2026