In this paper we consider the initial-boundary value problem for the higher-order degenerate quasilinear parabolic equation \frac{∂u(x, t)}{∂t} + Σ_{|α|≤M}(-1)^{|α|}D^αA_α(x, t, δu, D^mu) = 0 Under some structural conditions for A_α(x, t, δu, D^mu), existence and uniqueness theorem are proved by applying variational operator theory and Galërkin method.
