RT Journal Article
T1 Green's function related to a n order linear differential equation coupled to arbitrary linear non local boundary conditions
A1 Cabada Fernández, Alberto
A1 López Somoza, Lucía
A1 Yousfi Khoumsi, Mouhcine
K1 Green’s function
K1 Non-local boundary conditions
K1 Boundary value problems
AB In this paper, we obtain the explicit expression of the Green’s function related to a general n-th order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, an n dimensional parameter dependence is also assumed. Moreover, some comparison principles are obtained. The explicit expression depends on the value of the Green’s function related to the two-point homogeneous problem; that is, we are assuming that when all the parameters involved on the boundary conditions take the value zero then the problem has a unique solution, which is characterized by the corresponding Green’s function g. The expression of the Green’s function G of the general problem is given as a function of g and the real parameters considered at the boundary conditions. It is important to note that, in order to ensure the uniqueness of the solution of the considered linear problem, we must assume a non-resonant additional condition on the considered problem, which depends on the non-local conditions and the corresponding parameters. We point out that the assumption of the uniqueness of the solution of the two-point homogeneous problem is not a necessary condition to ensure the existence of the solution of the general case. Of course, in this situation, the expression we are looking for must be obtained in a different manner. To show the applicability of the obtained results, a particular example is given.
PB MDPI
SN 2227-7390
YR 2021
FD 2021-08-15
LK https://hdl.handle.net/10347/37959
UL https://hdl.handle.net/10347/37959
LA eng
NO Cabada, A.; López-Somoza, L.; Yousfi, M. Green’s Function Related to a n-th Order Linear Differential Equation Coupled to Arbitrary Linear Non-Local Boundary Conditions. Mathematics 2021, 9, 1948.
NO Xunta de Galicia (Spain), project EM2014/032
DS Minerva
RD 27 abr 2026