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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] C. M. Ablow, and C. L. Perry, Iterative solutions of the Diriehlet problem for $ \Delta u = {u^2}$, SIAM Journal, 7 (1959) 459 MR 0110214
  • [2] R. Courant, and D. Hilbert, Methods of mathematical physics, Vol. 2, Intersoience, N. Y., 1962
  • [3] L. Collatz, The numerical treatment of differential equations, Springer-Verlag, Berlin, 1960 MR 784038
  • [4] L. Bers, On mildly nonlinear partial differential equations of elliptic type, Jour. Res. N. B. S., 51, (1953) No. 5 MR 0064291
  • [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

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65.66

Retrieve articles in all journals with MSC: 65.66

Additional Information

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

American Mathematical Society