**
J. Rákosník (ed.), **

Function spaces, differential operators and nonlinear analysis.

Proceedings of the conference held in Paseky na Jizerou, September 3-9, 1995.

Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha 1996

p. 245 - 250

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A semilinear elliptic problem in an unbounded domain

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Klaus Pflüger

Freie Universität Berlin, Institut für Mathematik I, Arnimallee 2-6, D 14195 Berlin, Germany pflueger@math.fu-berlin.de

**Abstract:** We study a semilinear elliptic boundary value problem in an unbounded domain of $R^{n}$ $(n \geq 3)$ which arises for example in electromagnetic wave propagation in fibres. We consider nonlinear boundary conditions of the form $\partial u / \partial n = Q(x) |u|^{q-1} u$ $(q>1)$. A Mountain Pass Lemma approach and a comparison argument are used to construct a nontrivial solution of this problem.

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