Electron. J. Diff. Eqns. Vol. 1996(1996), No. 10, pp. 1-9.

A Dirichlet problem in the strip

Eugenio Montefusco

In this paper we investigate a Dirichlet problem in a strip and, using the sliding method, we prove monotonicity for positive and bounded solutions. We obtain uniqueness of the solution and show that this solution is a function of only one variable. From these qualitative properties we deduce existence of a classical solution for this problem.

Submitted June 8, 1996. Published October 26, 1996.
Math Subject Classification: 35J65, 35B50.
Key Words: Maximum Principle, Sliding Method, Subsolution and Supersolution.

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Eugenio Montefusco
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
e-mail: montefus@cibs.sns.it
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