Modified quasi-boundary value method for a Cauchy problem of semi-linear elliptic equation

2012 ◽  
Vol 89 (12) ◽  
pp. 1689-1703 ◽  
Author(s):  
H. W. Zhang
Keyword(s):  
Cauchy Problem ◽  
Elliptic Equation ◽  
Boundary Value ◽  
Linear Elliptic Equation ◽  
Boundary Value Method

Modified Boundary Value Problems For a Quasi-Linear Elliptic Equation

1956 ◽  
Vol 8 ◽  
pp. 203-219 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Continuous Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Linear Elliptic Equation ◽  
Partial Differential

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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