This article is cited in 17 papers

On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics

E. M. Varfolomeev

Peoples Friendship University of Russia

Abstract: 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.

UDC: 517.956.4

 English version: Journal of Mathematical Sciences, 2008, 153:5, 649–682

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