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The Dirichlet problem for a class of elliptic difference equations

Author: G. T. McAllister
Journal: Math. Comp. 25 (1971), 655-673
MSC: Primary 39A12; Secondary 35J20
MathSciNet review: 0306747
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Abstract: Under suitable assumptions on the order of nonlinearity we prove existence and uniqueness theorems for difference Dirichlet problems of divergence type. We also show that the discrete solutions converge to a solution of the continuous problem. We do not assume that our equation comes from a variational problem. Some of our results are constructive or allow for the application of constructive methods.

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Keywords: Elliptic difference equations, divergence type, approximation of solution, boundary-value problems, convergence of solution, existence, uniqueness criteria
Article copyright: © Copyright 1971 American Mathematical Society