Systems of the following form are studied \[ -(\phi(u'))' \in \partial F(t,u), \quad t\in [0,T], \quad l(u,u')=0, \] where \(l(u,u')\) denotes the Dirichlet, Neumann or periodic boundary conditions and \(\phi : B(0,a) \to \mathbb{R}^n\) is an homeomorphism such that \(\phi = \nabla\Phi\), with \(\Phi\) of class \(C^1\) and strictly convex. Here, \(\partial F\) is the generalized Clarke gradient of \(F(t,\cdot)\), a locally Lipschitzian map. Many existence results are obtained. Using nonsmooth critical theory, solutions are obtained as minimizers, saddle points or mountain pass points of associated functionals. Also, results are illustrated in examples of problems having Filippv solutions.