Solvability of discrete Dirichlet problem via lower and upper functions method

We use the lower and upper functions method to prove the existence of a solution of the Dirichlet problem where , , is positive and is continuous. Provided f fulfils certain sign conditions we get the solvability of the problem for each .

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Bibliographic Details
Published in:Journal of difference equations and applications 2007-05, Vol.13 (5), p.423-429
Main Authors: Rachunkova, Irena, Rachunek, Lukas
Format: Article
Language:English
Subjects:
Brouwer fixed point theorem
Dirichlet discrete BVP
Existence
Lower and upper functions
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Summary:We use the lower and upper functions method to prove the existence of a solution of the Dirichlet problem where , , is positive and is continuous. Provided f fulfils certain sign conditions we get the solvability of the problem for each .
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190601143302