Difference methods for a nonlinear elliptic system of partial differential equations

McAllister, G. T.

doi:10.1090/qam/189271

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 \[ \Delta {u_k} = {b_k}\prod \limits _{l = 1}^m {u_l^{n\left ( l \right )}} ,k = 1,...,m\left ( * \right )\] where the ${b_k}$ and the Dirichlet data ${u_k} = {\varphi _k}$ are non-negative.

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