THE METHOD OF SMALL PARAMETER IN DIRICHLET'S PROBLEM FOR A CERTAIN CLASS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER

Jan Bochenek, Alicja Pieniqzek
1974 Demonstratio Mathematica  
Let SI be a bounded domain in the n-dimensional Euclidean space E n . We assume, that the boundary T of the domain £2 is an (n -1) dimensional sufficiently regular surface. We denote by and A2 positive definite self-adjoint elliptic differential operators of the second order with constant coefficients. In the present paper we shall solve the boundary-value problem where du d is the transversal derivative of the function u with respect to the operator A2. This problem, will be analysed by means
more » ... analysed by means of the small parameter method. This method is applied in C7] to the biharmonic equation. The results of this paper generalize the results given.in [7] . To solve the problem (1) let us consider a problem depending on the parameter £ in the boundary condition (2) A-jAgU = f, u = 0, A2u = £(M du d + A2u) -167 -
doi:10.1515/dema-1974-0204 fatcat:oyhsc3xiozanfoowq24a2qxx4q