Geodesic
On a nonlinear nonlocal problem of elliptic type
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 417-428

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The solvability of a nonlinear nonlocal problem of the elliptic type that is a generalized Bitsadze–Samarskii-type problem is analyzed. Theorems on sufficient solvability conditions are stated. In particular, a nonlocal boundary value problem with $p$-Laplacian is studied. The results are illustrated by examples considered earlier in the linear theory (for $p=2$). The examples show that, in contrast to the linear case under the same “nice” nonlocal boundary conditions, for $p>2$, the problem can have one or several solutions, depending on the right-hand side. 
@article{ZVMMF_2017_57_3_a5,
     author = {O. V. Solonukha},
     title = {On a nonlinear nonlocal problem of elliptic type},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {417--428},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a5/}
}
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O. V. Solonukha. On a nonlinear nonlocal problem of elliptic type. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 417-428. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a5/