Strongly nonlinear multivalued elliptic equations on a bounded domain (Q742146)

The authors discuss the existence of nontrivial solutions for multivalued problems \[ -\text{div}(\phi(|\nabla u|)\nabla u) -b(u)u \in \lambda \partial F(x, u) \text{ for } \;x\in \Omega, \] where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\), and \(\partial F(x, t)\) is the generalized gradient of \(F(x,t)\) with respect to \(t\).