Geodesic
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.

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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 $\mathbb C\times\mathbb R^+$. 
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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/

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[5] Dang Khan Khoi, “O periodicheskikh resheniyakh nekotorykh nelineinykh evolyutsionnykh estestvennykh differentsialnykh uravnenii na mnogomernom tore”, Vestn. Novg. gos. un-ta., ser. Tekhn. nauki, 28 (2004), 77–79