Geodesic
A linear inverse problem for a mixed type operator-differential equation with a parameter
Matematičeskie zametki SVFU, Tome 23 (2016), pp. 3-18

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We study the inverse problem $$Bu_t+pLu=\varphi (t)+f(t, p),\quad u(0, p)=u(T,p)=0.$$ The operators $B,\,L$ are selfadjoint in the Hilbert space $E$ and the spectrum of the operator $L$ is semibounded. The unique solvability of this problem is proved with using a series expansion in eigen and associated elements of the pencil $L-\lambda B.$
Keywords: inverse problem, mixed type equation. 
@article{SVFU_2016_23_a0,
     author = {N. L. Abasheieva},
     title = {A linear inverse problem for a mixed type operator-differential equation with a parameter},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {23},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_a0/}
}
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N. L. Abasheieva. A linear inverse problem for a mixed type operator-differential equation with a parameter. Matematičeskie zametki SVFU, Tome 23 (2016), pp. 3-18. http://geodesic.mathdoc.fr/item/SVFU_2016_23_a0/