Minimal and maximal solutions for Dirichlet pseudomonotone problems
The following Dirichlet problem \[ -\text{div } a(x,u, Du)=f, \qquad u-u_0 \in W^{1,p}_0(\Omega), \] is studied. The problem does not have a unique solution in general. The existence of a minimal and maximal solution under some conditions for \(a\) is proved.
scientific article; zbMATH DE number 1556809
scientific article