Small periodic solutions of nonlinear systems of differential equations with constant deviation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 56-65
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We consider a nonlinear system of differential
equations in a general case with a singular matrix at the derivatives,
with a vector deviation which depends on a parameter. We seek for a
periodic solution to the system in the set of trigonometric series
such that the sequences of their coefficients belong to the space $l_1$.
We use the method, representing a space as a direct sum of subspaces,
and the method of a fixed
point of a nonlinear
operator as the main investigation techniques.
We reduce the question on the existence of a periodic solution to that
of the solvability of an operator equation, whose principal part is
defined in a
finite-dimensional space.
Keywords:
a vector form, an eigen element and an eigenvalue of an operator, a basis of a space, the projecting operator, linear functionals, a fixed point of an operator, the rank of a matrix.
@article{IVM_2008_6_a5,
author = {M. T. Terekhin},
title = {Small periodic solutions of nonlinear systems of differential equations with constant deviation},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {56--65},
publisher = {mathdoc},
number = {6},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2008_6_a5/}
}
TY - JOUR AU - M. T. Terekhin TI - Small periodic solutions of nonlinear systems of differential equations with constant deviation JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2008 SP - 56 EP - 65 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2008_6_a5/ LA - ru ID - IVM_2008_6_a5 ER -
M. T. Terekhin. Small periodic solutions of nonlinear systems of differential equations with constant deviation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 56-65. http://geodesic.mathdoc.fr/item/IVM_2008_6_a5/