A Dirichlet problem in the strip

Abstract

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.

Keywords

• Maximum Principle
• Sliding Method
• Subsolution and Supersolution.