JournalszaaVol. 16, No. 4pp. 919–943

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

  • R. Spielmann

    Technische Universität Dresden, Germany
A Semilinear Elliptic Equation with Dirac Measure as Right-Hand Side cover
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Abstract

We investigate solutions to the problem

Δu=λeu^+mδ   in D(Ω)\Delta u = \lambda eû + m \delta \ \ \ \mathrm {in} \ \mathcal D' (\Omega)
u=g   a.e.on Ω,u=g \ \ \ \mathrm {a.e. on} \ \partial \Omega,

where δ\delta is the Dirac measure and λ,m\lambda, m are real parameters, m>0m > 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