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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.
##### MSC:
 45K05 Integro-partial differential equations 30E25 Boundary value problems in the complex plane