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ON POSITIVENESS OF GREEN FUNCTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION

Annotation

We consider the two-point boundary value problem for a functional-differential equation. A necessary and sufficient condition for the negativity of the Green function in terms of the eigenvalues of two auxiliary problems is obtained.

Keywords

Green function; functional differential equation

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UDC

517.929.7

Pages

1246-1249

References

1. Labovskiy S., Volinsky I. On positivity of Green functions for a functional-differential equation // Functional Differential Equations. 2014. №21 (1–2). P. 17–30. 2. Labovskiy S. On positivity of the Green operator for functional differential equation // Functional Differential Equations. 2012. №19 (3-4). P. 323–333. 3. Labovskij S.M. O differencial'nyh neravenstvah dlja uravnenija s zapazdyvajushhim argumentom // Trudy Moskovskogo instituta himicheskogo mashinostroenija. 1975. № 64. C. 40–45. 4. Labovskij S.M. O sohranenii znaka vronskiana fundamental'noj sistemy, funkcii Koshi i funkcii Grina dvuhtochechnoj kraevoj zadachi dlja uravnenija s zapazdyvajushhim argumentom // Differencial'nye uravnenija. 1975. №11(10). C. 1780–1789. 5. Simonov P.M., Chistjakov A.V. O nekotoryh priznakah sohranenija znaka funkcii Grina dlja differencial'nogo uravnenija vtorogo porjadka s zapazdyvajushhim argumentom // Nekotorye problemy fundamental'noj i prikladnoj matematiki. M.: Moskovskij fiziko-tehnicheskij institut (gosudarstvennyj universitet), 1999. 6. Labovskij S.M. O linejnyh differencial'nyh neravenstvah. PhD thesis, Matematicheskij institut im. Razmadze. Tbilisi, 1975. 7. Krasnosel’skii M., Lifshits E., Sobolev A. Positive linear systems. The method of positive operators. Transl. from the Russian by J¨urgen Appell. Berlin: Heldermann-Verlag, 1989. Zbl 0674.47036. 8. Labovskij S.M. O polozhitel'nyh reshenijah linejnyh funkcional'no-differencial'nyh uravnenij // Differencial'nye uravnenija. 1984. №20(4). C. 578–584. 9. Labovskij S.M. Polozhitel'nye reshenija dvuhtochechnoj kraevoj zadachi dlja singuljarnogo linejnogo funkcional'no-differencial'nogo uravnenija // Differencial'nye uravnenija. 1988. №24(10). C. 1116–1123. 10. Krejn M.G., Rutman M.A. Vpolne nepreryvnye operatory, ostavljajushhie invariantnym konus v prostranstve Banaha // Uspehi matematicheskih nauk. 1948. №1(23). C. 3–95.

Received

2015-06-09

Section of issue

Scientific articles

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