Abstract
The article presents the results of study the existence of the solution of nonlinear problem for elliptic by Petrovsky system in unbounded domain. The nonlinear elliptic system is transformed into an equivalent fixed point problem for a suitable nonlinear operator in a convex subset of a Banach function space. Applying the fixed point and embedding theorems the solvability of nonlinear problem for elliptic by Petrovsky system in weighted Sobolev space are established.
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