Geodesic
Solvability of autonomous differential equation with aftereffect on negative semi-axis
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 26-37

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

We consider a linear autonomous homogeneous functional differential equation on the real negative semi-axis. We prove that if solutions belong to the special space of functions with integral limitations, then the space of solutions is finite-dimensional and its basis is formed by the solutions of the form $(t^m\exp(pt))$ generated by the roots of the characteristic equation. In contrast to the spaces used earlier, the pointwise estimation of solutions is replaced by the integral one. We adduce examples of differential equations with aftereffect and give the effective description of the space of solutions for these equations.
Keywords: functional differential equation, aftereffect, solvability on the axis, space of functions with exponential weight. 
@article{IVM_2017_10_a3,
     author = {A. S. Balandin and T. L. Sabatulina},
     title = {Solvability of autonomous differential equation with aftereffect on negative semi-axis},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {26--37},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_10_a3/}
}
TY  - JOUR
AU  - A. S. Balandin
AU  - T. L. Sabatulina
TI  - Solvability of autonomous differential equation with aftereffect on negative semi-axis
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 26
EP  - 37
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_10_a3/
LA  - ru
ID  - IVM_2017_10_a3
ER  - 
%0 Journal Article
%A A. S. Balandin
%A T. L. Sabatulina
%T Solvability of autonomous differential equation with aftereffect on negative semi-axis
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 26-37
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_10_a3/
%G ru
%F IVM_2017_10_a3
A. S. Balandin; T. L. Sabatulina. Solvability of autonomous differential equation with aftereffect on negative semi-axis. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 26-37. http://geodesic.mathdoc.fr/item/IVM_2017_10_a3/