Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Difference methods for a nonlinear elliptic system of partial differential equations


Author: G. T. McAllister
Journal: Quart. Appl. Math. 23 (1966), 355-359
MSC: Primary 65.66
DOI: https://doi.org/10.1090/qam/189271
MathSciNet review: 189271
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Abstract: This paper proves the existence and uniqueness of non-negative solutions to the Dirichlet problem associated with the nonlinear elliptic system

$\displaystyle \Delta {u_k} = {b_k}\prod\limits_{l = 1}^m {u_l^{n\left( l \right)}} ,k = 1,...,m\left( * \right)$

where the $ {b_k}$ and the Dirichlet data $ {u_k} = {\varphi _k}$ are non-negative.

References [Enhancements On Off] (What's this?)

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  • [5] D. Greenspan, Introductory numerical analysis of elliptic boundary value problems, Harper and Row, 1965 MR 0179956
  • [6] S. I. Pohazaev, The Diriehlet problem for the equation $ \Delta u = {u^2}$, Soviet Mathematics, 1 (1960) 1143 MR 0124610

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DOI: https://doi.org/10.1090/qam/189271
Article copyright: © Copyright 1966 American Mathematical Society

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