Electronic Journal of Differential Equations, Conference 06 (2001), pp. 313-342. Title: Generalized boundary value problems for nonlinear elliptic equations Authors: Laurent Veron (Faculte des Sciences et Techniques, Tours, France) Abstract: We give here an overview of some recent developments in the study of the description of all the positive solutions of \begin{equation} -\Delta u+|u|^{q-1}u=0 \label{NLE} \end{equation} in a domain $\Omega$ where $q>1$. Published January 8, 2001. Math Subject Classifications: 35J60, 35J67, 35D05. Key Words: Dirichlet Problem; Radon and Borel measures.