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

1983
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Demonstratio Mathematica
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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

doi:10.1515/dema-1983-0310
fatcat:3nyzh7ocqbdo3lgguec5p67awq