Geodesic
On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 248-263

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Nonlocal elliptic problems in plane domains are considered. Necessary conditions for the Fredholm solvability of such problems in weighted spaces are obtained. 
@article{TM_2008_260_a16,
     author = {A. L. Skubachevskii},
     title = {On {Necessary} {Conditions} for the {Fredholm} {Solvability} of {Nonlocal} {Elliptic} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {248--263},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a16/}
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A. L. Skubachevskii. On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 248-263. http://geodesic.mathdoc.fr/item/TM_2008_260_a16/