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A Dirichlet problem in the strip. (English) Zbl 0854.35043
Summary: 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.
MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
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