Geodesic
Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2019), pp. 3-18

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We obtain necessary and sufficient condition of solvability for a linear autonomous inhomogeneous functional differential equation with aftereffect and find the representation of all solutions in the special space of integrable functions with exponential weight. The obtained results are applied for study of two inhomogeneous differential equations with delay (the first equation is with concentrated delay, and the second one is with distributed delay). We give effective description of the space of solutions for these equations.
Keywords: functional differential equation, aftereffect, inhomogeneous equation, solvability on the axis, space of functions with exponential weight. 
@article{IVM_2019_3_a0,
     author = {A. S. Balandin and T. L. Sabatulina},
     title = {Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--18},
     publisher = {mathdoc},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_3_a0/}
}
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A. S. Balandin; T. L. Sabatulina. Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2019), pp. 3-18. http://geodesic.mathdoc.fr/item/IVM_2019_3_a0/