Geodesic
A Dirichlet problem in the strip
Electronic journal of differential equations, Tome 1996 (1996) no. 10
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.
Classification : 35J65, 35B50
Keywords: maximum principle, sliding method, subsolution and supersolution 
@article{EJDE_1996__1996_10_a0,
     author = {Montefusco,  Eugenio},
     title = {A {Dirichlet} problem in the strip},
     journal = {Electronic journal of differential equations},
     year = {1996},
     volume = {1996},
     number = {10},
     zbl = {0854.35043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1996__1996_10_a0/}
}
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%J Electronic journal of differential equations
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Montefusco,  Eugenio. A Dirichlet problem in the strip. Electronic journal of differential equations, Tome 1996 (1996) no. 10. http://geodesic.mathdoc.fr/item/EJDE_1996__1996_10_a0/