On the spectral problem and positive solutions for a functional-differential equation of the even order

M. J. Alves^a, S. M. Labovski<sup>b

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

Abstract: Basic properties of the system of eigenfunctions for even order functional differential equation under special boundary conditions are obtained. Equivalence of a serie of classical affirmations is established. Among them are the Vallee-Poussin affirmation and positivity of the corresponding quadratic functional.

Keywords: quadratic functional, Vallee-Poussin theorem, functional differential operator, spectrum.

UDC: 517.929.7

Received: 22.03.2018

DOI: 10.20310/1810-0198-2018-23-122-154-157

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