Some remarks on critical point theory for nondifferentiable functionals (Q1288186)

The authors study the existence of critical points of nondifferentiable functionals \(J\) of the kind \[ J(v)= \int_\Omega A(x,v)|\nabla v|^2- F(x,v) \] with \(A(x,v)\) a Carathéodory function bounded between positive constant and with bounded derivative respect to the variable \(z\), and \(F(x,z)\) is the primitive of a (Carathéodory) nonlinearity \(f(x,z)\) satisfying suitable hypotheses. Since \(J\) is just differentiable along bounded directions, a suitable compactness condition is introduced.