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On the solvability of degenerated quasilinear elliptic equations of higher order. (English) Zbl 0847.35054
The authors prove existence of a solution to the nonlinear degenerated elliptic boundary value problem $\sum_{|\alpha|\leq m} (- 1)^{|\alpha|} D^\alpha A_\alpha(x, u,\dots, D^m u)= \sum_{|\alpha|\leq m} (- 1)^{|\alpha|} D^\alpha f_\alpha(x)\quad\text{in} \quad \Omega,$ in a closed subspace $$V$$ of the weighted Sobolev space $$W^{1, p}(\Omega; \nu)$$. The proof uses degree theory arguments.

##### MSC:
 35J70 Degenerate elliptic equations 35J65 Nonlinear boundary value problems for linear elliptic equations
##### Keywords:
existence; weighted Sobolev space; degree theory
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