On the reduction procedure for a nonlinear integro-differential equation
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.
scientific article; zbMATH DE number 4069546