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Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto
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1. Introduction. The quasi-linear elliptic partial differential equation to be studied here has the form

(1.1) Δu = − F(P,u).

Here Δ is the Laplacian while F(P,u) is a continuous function of a point P and the dependent variable u. We shall study the Dirichlet problem for (1.1) and will find that the usual formulation must be modified by the inclusion of a parameter in the data or the differential equation, together with a further numerical condition on the solution.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 203 - 219
Copyright
Copyright © Canadian Mathematical Society 1956

References

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