Estimates for solutions of retarded equations with variable coefficients
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 83-93.

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

In this work, we study retarded-type differential-difference equations with variable coefficients. Using the adjoint equation, we obtain an integral representation of the solution. A number of results on the asymptotic behavior of the solutions is proved on the basis of this representation.
@article{FPM_2006_12_5_a7,
     author = {A. A. Lesnykh},
     title = {Estimates for solutions of retarded equations with variable coefficients},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a7/}
}
TY  - JOUR
AU  - A. A. Lesnykh
TI  - Estimates for solutions of retarded equations with variable coefficients
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 83
EP  - 93
VL  - 12
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a7/
LA  - ru
ID  - FPM_2006_12_5_a7
ER  - 
%0 Journal Article
%A A. A. Lesnykh
%T Estimates for solutions of retarded equations with variable coefficients
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 83-93
%V 12
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a7/
%G ru
%F FPM_2006_12_5_a7
A. A. Lesnykh. Estimates for solutions of retarded equations with variable coefficients. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 83-93. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a7/

[1] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl

[2] Vlasov V. V., “O razreshimosti i svoistvakh reshenii funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Mat. sb., 186:8 (1995), 67–92 | MR | Zbl

[3] Zverkin A. M., “Razlozhenie v ryad reshenii lineinykh differentsialno-raznostnykh uravnenii”, Tr. sem. po teorii differents. uravnenii s otklonyayuschimsya argumentom, 4, 1967, 3–50 | MR | Zbl

[4] Kolmanovskii V. B., Nosov V. R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, M., 1981 | MR

[5] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR | Zbl

[6] Pinni E., Obyknovennye differentsialno-raznostnye uravneniya., Izd. inostr. lit., M., 1961 | MR

[7] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR

[8] Elsgolts E. L., Norkin S. B., Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M, 1971 | MR

[9] Banks H. T., “The representation of solutions of linear functional differential equations”, J. Differential Equations, 5 (1969), 399–410 | DOI | MR

[10] Bellman R., Cooke K. L., “Stability theory and adjoint operators for linear differential-difference equations”, Trans. Amer. Math. Soc., 92 (1959), 470–500 | DOI | MR | Zbl

[11] Bellman R., Cooke K. L., “rAsymptotic Behavior of Solutions of Differential-Difference Equations”, Mem. Amer. Math. Soc., Amer. Math. Soc., 35 (1959) | MR | Zbl

[12] Hale J. K., Meyer K. R., “A Class of Functional Equations of Neutral Type”, Mem. Amer. Math. Soc., Amer. Math. Soc., 76 (1967) | MR | Zbl

[13] Vlasov V. V., “Spectral problems arising in the theory of differential equations with delay”, J. Math. Sci., 124:4 (2004), 5176–5192 | DOI | MR

[14] Wright E. M., “The linear difference-differential equation with asymptotically constant coefficients”, Amer. J. Math., 70 (1948), 221–238 | DOI | MR | Zbl

[15] Wright E. M., “Perturbed functional equations”, Quart. J. Math., 20 (1949), 155–165 | DOI | MR | Zbl