Critical point theory for nonsmooth functionals (Q876949)

The authors develop critical point theory for nonsmooth potentials \(f\colon H^1_0(\Omega)\longrightarrow\mathbb{R}\) of the form \(f(u)=\frac{1}{2}\int_{\Omega}\sum\limits_{i,j=1}^na_{ij}(x,u)D_iuD_ju\,dx-\int_{\Omega}G(x,u)\,dx\). First, the corresponding deformation lemma is proved. Next, a saddle point theorem is proved for functionals defined on a product space.