Geodesic
On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects
Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 3-19.

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We obtain necessary and sufficient conditions for the continuous invertibility and the Fredholm property of operators generated by a family of evolution operators, with boundary conditions given by a linear relation and impulse effects also given by a linear relation.
Keywords: continuous invertibility, Fredholm property, family of evolution operators, linear relation, impulse effect. 
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V. B. Didenko. On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects. Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a1/

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