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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 4, 1997, pp. 919–943
DOI: 10.4171/ZAA/797

Published online: 1997-12-31

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

R. Spielmann[1]

(1) Technische Universität Dresden, Germany

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.

Keywords: GeIfand equation with Dirac measure, distributional solutions, existence and multiplicity results, phase plane analysis

Spielmann R.: A Semilinear Elliptic Equation with Dirac Measure as Right-Hand Side. Z. Anal. Anwend. 16 (1997), 919-943. doi: 10.4171/ZAA/797