Geodesic
Substantiation of Fourier method in mixed problem with involution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 3-12

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In this paper the mixed problem for the first order differential equation with involution is investigated. Using the received specified asymptotic formulas for eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to transform a series representing the formal solution on Fourier method, and to prove the possibility of its term by term differentiation. At the same time on the initial problem data minimum requirements are imposed. 
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     author = {M. Sh. Burlutskaya and A. P. Khromov},
     title = {Substantiation of {Fourier} method in mixed problem with involution},
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M. Sh. Burlutskaya; A. P. Khromov. Substantiation of Fourier method in mixed problem with involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 3-12. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a0/