Some PDEs problems in generalized Sobolev algebras (Q663613)

The authors consider the following Dirichlet problem \[ \begin{cases} -\Delta \Phi (u)+\Psi (u)=f\text{ in }\Omega , \\ u=g\text{ on }\partial \Omega , \end{cases}\tag{1} \] where \(\Omega \) is an open bounded domain of \(\mathbb{R}^{d}\)\ with Lipschitz continuous boundary, \(\Phi \) and \(\Psi \) are increasing real valued differentiable functions defined on \(\mathbb{R}.\) The problem (1) is studied in the framework of the \((\mathcal{C},\mathcal{E}, \mathcal{P})\)-algebras of generalized functions of Sobolev type.