Geodesic
Solvability analysis of a nonlocal boundary value problem by applying the contraction mapping principle
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1679-1683

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The existence and uniqueness of a classical solution to the nonlocal boundary value problem for Poisson's operator on a two-dimensional rectangular domain is proved in detail by applying the contraction mapping principle. 
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     author = {E. A. Volkov},
     title = {Solvability analysis of a nonlocal boundary value problem by applying the~contraction mapping principle},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {10},
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E. A. Volkov. Solvability analysis of a nonlocal boundary value problem by applying the contraction mapping principle. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1679-1683. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a7/