Geodesic
On the solvability of some nonlinear elliptic problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 404-416

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The solvability of second-order nonlinear elliptic equations in weighted Sobolev spaces is analyzed. An additional condition ensuring the solvability of such equations is that the average of the desired solution over some circle of fixed radius is zero. Examples are equations containing a weighted $p$-Laplacian and the Euler equations. 
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     author = {E. V. Golubeva and Yu. A. Dubinskii},
     title = {On the solvability of some nonlinear elliptic problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {404--416},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a4/}
}
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E. V. Golubeva; Yu. A. Dubinskii. On the solvability of some nonlinear elliptic problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 404-416. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a4/