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JOURNALS // Russian Universities Reports. Mathematics // Archive

Tambov University Reports. Series: Natural and Technical Sciences, 2018 Volume 23, Issue 121, Pages 5–9 (Mi vtamu85)

Scientific articles

On discreteness of spectrum of a second order functional differential operator

S. M. Labovski

Plekhanov Russian University of Economics

Abstract: Necessary and sufficient conditions for discreteness of spectrum for the singular second order functional differential operator of the form
$$ \frac{1}{\rho(x)}\left(-(p(x)u')'+q(x)u-\int_a^b u(s)r(x,ds)\right), \; x\in (a,b),\; -\infty\le a<b\le\infty $$
are obtained.

Keywords: discreteness of spectrum, functional differential operator.

UDC: 517.929.7

Received: 18.01.2018

Language: English

DOI: 10.20310/1810-0198-2018-23-121-5-7



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© Steklov Math. Inst. of RAS, 2025