Existence results for nonlinear elliptic problems with lower order terms (Q2923063)

The paper deals with existence of entropy solutions of nonlinear equations of the form NEWLINE\[NEWLINE -\mathrm{div}\big( a(x,u,\nabla u)+\Phi(u)\big)+g(x,u,\nabla u)+H(x,\nabla u)=\mu\quad \mathrm{in}\;\Omega, NEWLINE\]NEWLINE where \(\mu\in L^1(\Omega)+W^{-1,p'}(\Omega),\) \(-\mathrm{div}(a(x,u,\nabla u)\big)\) is a Leray-Lions operator growing as \(|\nabla u|^{p-1}\) and \(\Phi\in C^0(\mathbb{R},\mathbb{R}^N).\) The term \(g(x,u,\nabla u)\) grows critically in \(|\nabla u|\) with no restrictions in \(u,\) while \(H(x,\nabla u)\sim |\nabla u|^{p-1}.\)