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

R. Spielmann

doi:10.4171/zaa/797

JournalszaaVol. 16, No. 4pp. 919–943

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

R. Spielmann
Technische Universität Dresden, Germany

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Abstract

We investigate solutions to the problem

Δ u = λ e \overset{u}{^} + m δ in D^{'} (Ω)

u = g a.e.on \partial Ω,

where $δ$ is the Dirac measure and $λ, m$ 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.

Cite this article

R. Spielmann, A Semilinear Elliptic Equation with Dirac Measure as Right-Hand Side. Z. Anal. Anwend. 16 (1997), no. 4, pp. 919–943

DOI 10.4171/ZAA/797