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Boundary value problems for integro-differential equations of Barbashin type. (English) Zbl 0808.45012

The solvability of linear integro-differential equations of Barbashin type subject to appropriate boundary conditions is considered. A transformation of such equations to linear two-dimensional integral equations of the second kind is given. Applying a general fixed point principle in \(K\)-normed spaces general existence results are established. The considerations are illustrated by an application to the problem of radiation propagation in physical systems.

MSC:

45J05 Integro-ordinary differential equations
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