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A classification for integral boundary value problems in wide band. (English. Russian original) Zbl 0835.45006
Russ. Math. 38, No. 5, 1-10 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 5(384), 3-12 (1994).
The authors study the integral boundary value problem: \(\partial u(x,y)/ \partial y = P (\partial/ \partial x) u(x,y)\), \((x,y) \in \pi_y\), \(Au(x,0) + Bu(x,Y) + C \int^y_0 u(x,y) dy = u_0 (x)\), \(x \in \mathbb{R}\), in the band \(\pi_Y = \mathbb{R} \times [0,Y]\) for a large \(Y > 0\), where \(u : \pi_Y \to \mathbb{C}\) and \(u_0 : \mathbb{R} \to \mathbb{C}\) are the unknown and given functions, respectively; \(P\) is an arbitrary polynomial with constant coefficients; \(Y > 0\), \(A,B\) and \(C\) are given complex constants, \(|A |+ |B |+ |C |> 0\).
A complete classification considering the asymptotically correct resolvability of the problem is given.
45K05 Integro-partial differential equations
30E25 Boundary value problems in the complex plane