First regularized trace of the limit assignment of Sturm-Liouville type with two constant delays | Zendy

Nataša Pavlović | Zendy; Milenko Pikula | Zendy; Biljana Vojvodić | Zendy

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First regularized trace of the limit assignment of Sturm-Liouville type with two constant delays

Author(s) -

Nataša Pavlović,

Milenko Pikula,

Biljana Vojvodić

Publication year - 2015

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1501051p

Subject(s) - mathematics , trace (psycholinguistics) , eigenvalues and eigenvectors , sturm–liouville theory , type (biology) , constant (computer programming) , limit (mathematics) , operator (biology) , function (biology) , combinatorics , mathematical analysis , mathematical physics , physics , quantum mechanics , chemistry , boundary value problem , ecology , philosophy , linguistics , biochemistry , repressor , evolutionary biology , computer science , transcription factor , gene , programming language , biology

We observe spectral assignment D2y = λy defined by -y''(x) + q1(x)y(x - τ1) + q2(x)y(x - τ2) = λy(x), λ = z2 (1) q1(x), q2(x) L1[0,π], τ1, τ2 (0,π) y(x -τ1)≡ 0, x (0, τ1], τ1 = k0τ2 (2), y(π) = 0 (3) In this paper, we construct a solution y(x, z) which satisfies (1) and (2), and then (3) is used to construct the characteristic function F(z), z C. Then the asymptotics of eigenvalues of the operator D2 is constructed. Finally, the first regularized trace is calculated.

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