We investigate solutions to the problem

$$
\Delta u = \lambda eû + m \delta \ \ \ \mathrm {in} \ \mathcal D' (\Omega)
$$

$$
u=g \ \ \ \mathrm {a.e. on} \ \partial \Omega,
$$

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.

A Semilinear Elliptic Equation with Dirac Measure as Right-Hand Side

R. Spielmann

Abstract

Cite this article