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Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1956
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