Geodesic
On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 93-98

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain new unimprovable effective conditions for the oscillation of all solutions of linear first-order differential and difference equations with several delays. We show that known results of the kind are consequences of the new results. We reveal the reasons for the impossibility to obtain oscillation conditions for equations with several delays, as sharp as the conditions for the equation with one delay, in case exceptionally known approaches used.
Keywords: differential equation, difference equation, aftereffect, equation with several delays
Mots-clés : oscillation, effective conditions. 
K. M. Chudinov. On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 93-98. http://geodesic.mathdoc.fr/item/IVM_2018_5_a10/
@article{IVM_2018_5_a10,
     author = {K. M. Chudinov},
     title = {On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {93--98},
     year = {2018},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_5_a10/}
}
TY  - JOUR
AU  - K. M. Chudinov
TI  - On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 93
EP  - 98
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_5_a10/
LA  - ru
ID  - IVM_2018_5_a10
ER  - 
%0 Journal Article
%A K. M. Chudinov
%T On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 93-98
%N 5
%U http://geodesic.mathdoc.fr/item/IVM_2018_5_a10/
%G ru
%F IVM_2018_5_a10

[1] Myshkis A. D., “O resheniyakh lineinykh odnorodnykh differentsialnykh uravnenii pervogo poryadka ustoichivogo tipa s zapazdyvayuschim argumentom”, Matem. sb., 28:3 (1951), 641–658

[2] Ladas G., “Sharp conditions for oscillations caused by delays”, Appl. Anal., 9:2 (1979), 93–98 | DOI | MR

[3] Koplatadze R. G., Chanturiya T. A., “Kolebaniya i monotonnye resheniya differentsialnykh uravnenii pervogo poryadka s otklonyayuschimsya argumentom”, Differents. uravneniya, 18:8 (1982), 1463–1465 | MR

[4] Ladas G., Lakshmikantham V., Papadakis J. S., “Oscillations of higher-order retarded differential equations generated by the retarded argument”, Delay and functional differential equations and their applications, Proc. Conf. (Park City, Utah), Academic Press, N. Y., 1972, 219–231 | DOI | MR

[5] Tramov M. I., “Usloviya koleblemosti reshenii differentsialnykh uravnenii pervogo poryadka s zapazdyvayuschim argumentom”, Izv. vuzov. Matem., 1975, no. 3, 92–96

[6] Ladde G. S., Lakshmikantham V., Zhang B. G., Oscillation theory of differential equations with deviating arguments, Marcel Dekker, New York, 1987 | MR

[7] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991

[8] Chudinov K., “Note on oscillation conditions for first-order delay differential equations”, Electron. J. Qual. Theory Diff. Eq., 2016, 2, 10 pp. | MR

[9] Zhang B. G., Tian Ch. J., “Nonexistence and existence of positive solutions for difference equations with unbounded delay”, Comput. Math. Appl., 36:1 (1998), 1–8 | DOI | MR

[10] Chatzarakis G. E., Koplatadze R., Stavroulakis I. P., “Optimal oscillation criteria for first order difference equations with delay argument”, Pacific J. Math., 235:1 (2008), 15–33 | DOI | MR

[11] Chatzarakis G. E., Koplatadze R., Stavroulakis I. P., “Oscillation criteria of first order linear difference equations with delay argument”, Nonlinear Anal., 68:4 (2008), 994–1005 | DOI | MR

[12] Fukagai N., Kusano T., “Oscillation theory of first order functional-differential equations with deviating arguments”, Ann. Mat. Pura Appl., 136:4 (1984), 95–117 | DOI | MR

[13] Grammatikopoulos M. K., Koplatadze R., Stavroulakis I. P., “On the oscillation of solutions of first order differential equations with retarded arguments”, Georgian Math. J., 10:1 (2003), 63–76 | MR

[14] Li B., “Oscillation of first order delay differential equations”, Proc. Amer. Math. Soc., 124:12 (1996), 3729–3737 | DOI | MR

[15] Stavroulakis I. P., “Oscillation criteria for delay and difference equations with non-monotone arguments”, Appl. Math. Comput., 226 (2014), 661–672 | MR

[16] Stavroulakis I. P., “Oscillations of delay and difference equations with variable coefficients and arguments”, Differential and difference equations with applications, Springer Proceedings in Mathematics Statistics, 164, 2016, 169–189 | DOI | MR

[17] Koplatadze R., Pinelas S., “Oscillation criteria for first-order linear difference equation with several delay arguments”, NelīnīĭnīKoliv., 17:2 (2014), 248–267 | MR

[18] Tang X. H., Yu J. S., “Oscillation of delay difference equation”, Comput. Math. Appl., 37:7 (1999), 11–20 | DOI | MR

[19] Chatzarakis G. E., Pinelas S., Stavroulakis I. P., “Oscillations of difference equations with several deviated arguments”, Aequationes Math., 88:1–2 (2014), 105–123 | DOI | MR

[20] Braverman E., Chatzarakis G. E., Stavroulakis I. P., “Iterative oscillation tests for difference equations with several non-monotone arguments”, J. Diff. Equat. Appl., 21:9 (2015), 854–874 | DOI | MR

[21] Braverman E., Chatzarakis G. E., Stavroulakis I. P., “Corrigendum to: Braverman E., Chatzarakis G. E., Stavroulakis I. P., Iterative oscillation tests for difference equations with several non-monotone arguments”, J. Diff. Equat. Appl., 21:9 (2015), 854–874 ; J. Diff. Equat. Appl., 2017 | DOI | MR | DOI