Geodesic
On the geometric nature of partial and conditional stability
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 76-85

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

We prove that certain problems which generalize the classical stability problem studied by A. M. Lyapunov admit a coordinate-free description. Namely, we mean problems on partial and conditional stability of solutions to vector functional differential equations, as well as a more general problem on the dependence of asymptotic properties of certain components of solutions on other ones. For equations in the form $$ x(t)-A\int^t_0x(s)d_sr(t,s)=f(t), $$ where the matrix $A=\mathrm{const}$ and $r:\{(t,s):0\le s\le t\}\to\mathbb C$, the indicated types of stability are defined by properties of minimal subspaces of the vector space which are invariant with respect to a given transformation and belong to a given subspace.
Keywords: functional differential equation, partial stability, conditional stability, invariant subspace. 
@article{IVM_2008_3_a6,
     author = {K. M. Chudinov},
     title = {On the geometric nature of partial and conditional stability},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--85},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_3_a6/}
}
TY  - JOUR
AU  - K. M. Chudinov
TI  - On the geometric nature of partial and conditional stability
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 76
EP  - 85
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_3_a6/
LA  - ru
ID  - IVM_2008_3_a6
ER  - 
%0 Journal Article
%A K. M. Chudinov
%T On the geometric nature of partial and conditional stability
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 76-85
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_3_a6/
%G ru
%F IVM_2008_3_a6
K. M. Chudinov. On the geometric nature of partial and conditional stability. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 76-85. http://geodesic.mathdoc.fr/item/IVM_2008_3_a6/