Consider the following quasilinear elliptic equation $$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$ on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\partial \Omega} = 0.$$

• Where can I find references on this kinds of problems (in particular about a variational approach to solve them)?
• What's the correct formulation of a "uniform ellipticity"-type condition that gives existence and uniqueness for this problem?