## A Dirichlet problem in the strip

### Summary

Summary: 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.

35J65, 35B50

### Keywords/Phrases

maximum principle, sliding method, subsolution and supersolution