On the reduction procedure for a nonlinear integro-differential equation (Q1109277)

Starting with a general linear Dirichlet problem for a second order strongly elliptic operator in a smooth \(n\)-dimensional domain, the author introduces an additional nonlinear term into the equation which is given by a real function \(f\), acting on a linear functional on the state, which in turn is nonzero on a particular ''fundamental'' solution. This one- dimensional perturbation problem is decoupled into a linear Dirichlet problem ans a scalar nonlinear equation. The solutions of the nonlinear perturbation problem can be given as combinations of both subproblems. No assumptions on the scalar function \(f\) are needed in principle.