Algebra i analiz, Tome 18 (2006) no. 4, pp. 83-94
Citer cet article
Dang Khanh Hoi. On the structure of the set of periods for periodic solutions of some linear integro-differential equations on the multidimensional sphere. Algebra i analiz, Tome 18 (2006) no. 4, pp. 83-94. http://geodesic.mathdoc.fr/item/AA_2006_18_4_a3/
@article{AA_2006_18_4_a3,
author = {Dang Khanh Hoi},
title = {On the structure of the set of periods for periodic solutions of some linear integro-differential equations on the multidimensional sphere},
journal = {Algebra i analiz},
pages = {83--94},
year = {2006},
volume = {18},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AA_2006_18_4_a3/}
}
TY - JOUR
AU - Dang Khanh Hoi
TI - On the structure of the set of periods for periodic solutions of some linear integro-differential equations on the multidimensional sphere
JO - Algebra i analiz
PY - 2006
SP - 83
EP - 94
VL - 18
IS - 4
UR - http://geodesic.mathdoc.fr/item/AA_2006_18_4_a3/
LA - ru
ID - AA_2006_18_4_a3
ER -
%0 Journal Article
%A Dang Khanh Hoi
%T On the structure of the set of periods for periodic solutions of some linear integro-differential equations on the multidimensional sphere
%J Algebra i analiz
%D 2006
%P 83-94
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/AA_2006_18_4_a3/
%G ru
%F AA_2006_18_4_a3
The problem of periodic solutions for the family of linear differential equations $$ (L-\lambda)u\equiv\biggl(\frac1i\frac\partial{\partial t}-a\Delta-\lambda\biggr)u(x,t)=\nu G(u-f) $$ is considered on the multidimensional sphere $x\in S^n$ under the periodicity condition $u|_{t=0}=u|_{t=b}$. Here $a$ and $\lambda$ are given reals, $\nu$ is a fixed complex number, $Gu(x,t)$ is a linear integral operator, and $\Delta$ is the Laplace operator on $S^n$. It is shown that the set of parameters $(\nu,b)$ for which the above problem admits a unique solution is a measurable set of full measure in $\mathbb C\times\mathbb R^+$.
