On the solvability of degenerated quasilinear elliptic equations of higher order (Q1327078)

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.