Geodesic
On a mixed type fourth-order differential equation
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 47 (2016) no. 1, pp. 119-128

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We consider questions of solvability and constructing the solution to a nonlocal mixed boundary value problem for a homogeneous mixed type fourth-order differential equation. We use the spectral method based on separation of variables. A criterion for unique solvability of the problem is obtained. We also study questions of existence of solutions in the case where uniqueness of the solution does not hold.
Keywords: boundary value problem, mixed type differential equation, fourth-order equation, integral conditions, unique solvability. 
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     author = {T. K. Yuldashev},
     title = {On a mixed type fourth-order differential equation},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {119--128},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2016_47_1_a4/}
}
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T. K. Yuldashev. On a mixed type fourth-order differential equation. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 47 (2016) no. 1, pp. 119-128. http://geodesic.mathdoc.fr/item/IIMI_2016_47_1_a4/