Scientific articles

On the spectral properties and positivity of solutions of a periodic boundary value problem for a second-order functional differential equation

M. J. Alves^a, S. M. Labovski<sup>b

a</sup> Eduardo Mondlane University
^b Plekhanov Russian University of Economics

Abstract: For a functional-differential operator
\begin{equation*} \mathcal{L} u = (1/\rho)\left(-(pu')'+\int_0^l u(s)d_s r(x,s)\right) \end{equation*}
with symmetry, the completeness and orthogonality of the eigenfunctions is shown. The positivity conditions of the Green function of the periodic boundary value problem are obtained.

Keywords: positive solutions, spectral properties.

UDC: 517.9

Received: 01.04.2020

DOI: 10.20310/2686-9667-2020-25-130-123-130