Geodesic
On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 5-36 
E. M. Varfolomeev. On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 5-36. http://geodesic.mathdoc.fr/item/CMFD_2007_21_a0/
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     author = {E. M. Varfolomeev},
     title = {On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics},
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Quasilinear parabolic functional differential equations containing multiple transformations of spatial variables are considered with the Neumann boundary-value conditions. Sufficient conditions of the Andronov–Hopf bifurcation of periodic solutions are obtained along with expansions of the solutions in powers of small parameter. Spectral properties of the linearized elliptic operator of this problem are investigated. Necessary and sufficient conditions of normality are obtained for such operators. Examples on their properties are given.

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