On the solvability of nonlinear elliptic equations in Sobolev spaces

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We consider the existence of solutions of the system (*)

P (D) u^{l} = F (x, (\partial^{α} u))

, l = 1,...,k,

x \in ℝ^{n}

(u = (u ¹, ..., u^{k}))

in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.

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