A semilinear elliptic equation with Dirac measure as right-hand side (Q1381107)

Summary: We investigate solutions to the problem \[ \Delta u= \lambda e^u+m \delta \text{ in } {\mathcal D}' (\Omega), \quad u=g\text{ a.e. on } \partial\Omega, \] where \(\delta\) is the Dirac measure and \(\lambda,m\) are real parameters, \(m>0\). We discuss the existence and uniqueness of solutions in dependence of these parameters. For the homogeneous Dirichlet problem in a ball we give multiplicity results.