Mappings of monotone type and nonlinear obstacle problem. (English) Zbl 0575.35024
A survey of recent developments in the study of the existence of solutions of nonlinear variational equations and inequalities for quasilinear elliptic operators of the form
\[
Au(x)=\sum_{| \alpha | \leq m}(-1)^{| \alpha |}D^{\alpha} A_{\alpha}(x,u(x),...,D^ mu(x)),\quad x\in \Omega \subset R^ N
\]
is given. We also sketch a Galerkin method which is useful for very strongly nonlinear operators, i.e. even the top order coefficients \(A_{\alpha}\) do not obey any polynomial growth condition.
MSC:
35J60 | Nonlinear elliptic equations |
49J40 | Variational inequalities |
47J25 | Iterative procedures involving nonlinear operators |