Geodesic
Representations of solutions of periodic partial differential equations
Izvestiya. Mathematics , Tome 21 (1983) no. 1, pp. 93-117

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A variant of the Floquet theory for partial differential equations is constructed. Exponentially increasing solutions of periodic hypoelliptic equations and systems are decomposed into integrals over Floquet solutions. Analogous results are obtained for equations with deviating argument and for boundary-value problems in domains of the periodic wave guide type. The question of nonzero $L_2(\mathbf R^n)$-solutions of equations in these classes is also examined. Bibliography: 41 titles. 
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     author = {P. A. Kuchment},
     title = {Representations of solutions of periodic partial differential equations},
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P. A. Kuchment. Representations of solutions of periodic partial differential equations. Izvestiya. Mathematics , Tome 21 (1983) no. 1, pp. 93-117. http://geodesic.mathdoc.fr/item/IM2_1983_21_1_a3/