ON THE LAURICELLA PROBLEM FOR THE EQUATION Δ2u(X)=f(X,u(X)) IN THE CIRCLE

Barański Feliks, Jan Musiałek
1983 Demonstratio Mathematica  
o In [l] the Lauricella problem for the equation A u(X) = = f(X) in the circle was solved. In the present paper we shall study the following Lauricella problem,in the cirole K = {x:|x| <R}, D .tt(X) = f5(X) for X e 3K, n X * where f,f^,f2 are given functions, n^ denotes the inward normal to 3K in the point Xe 3K. 2. Using the convenient Green function G, we shall replace the problem (1) -(3) by an integral equation which may be solved by the Banach method of the contracting mapping. Let us
more » ... apping. Let us denote: X = (x-pxg) is an arbitrary point of K, Y = (yvy2) ia an arbitrary point of the plane E^, X = (x1fx2) is the symmetric image of X with respect to 3K, r 2 (X;Y) = (y1-x1) 2 + (y2-x2) 2 , A = -(2R 2 )' 1 , B(X) = R 2 -r 2 (0;X), -677 -Unauthenticated Download Date | 2/26/20 3:45 AM
doi:10.1515/dema-1983-0310 fatcat:3nyzh7ocqbdo3lgguec5p67awq